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product rule simplification

Please provide step by step solution. Thank you! Algebra Chapter 09 1. Use the product rule to simplify √12x^8 2. Evaluate the expression 25-3/2 3. Simplify the expression √2t5 * √10t4 4. Divide and simplify √14/√7 5. Solve and check for extraneous solutions √a-1-5=1 Chapter

Derivatives, Tangents and Rate of Change

All solutions must be detailed and the final answers simplified. Show all work! 1. Differentiate the given function. Simplify your answer. 2. Differentiate the given function. Simplify your answer. 3. Differentiate the given function. Simplify your answer. 4. Find the equation of the line that is ta

Rate of Change..

If $10,000 is invested at an annual rate r(expressed as decimal) compound weekly, the total amount (principal P and interest) accumulated after 10 years is given by the formula. A=10,000(1+r/52)^520 A.Find the rate of change of A with respect to r. B.Find the percentage rate of change of A with respe

Tangent Lines: Example Problem

Find an equation for the tangent line at the given curve at the point where x=x0; a. y=(x^2+3x-1)(2-x); x0=1 b. y=x+7/5-2x; x0;=0 Find all points on the given graph of the given function where the tangent line is horizontal. f(x)=(x-1)(x^2-8x+7)

Function, derivatives, error, and stationary points.

See attached. Consider the function of two real variables x and y (y not 1) defined by.... Find the first-order and second-order partial derivatives of f. Determine the second-order Taylor polynomial for f near (0,-1) Use first-order partial derivatives to determine the least and greatest possible values. Use the chain ru

Differentiate the functions

Please see the attached file for the fully formatted problems. Differentiate the functions. 1. g(t) = ( )1/2 g(t) = (3t5)-1/2 g(t) = 3t-5/2 g'(t) = t-7/2 2. ****There is a closing bracket after 4. Where is the open bracket? It is necessary to see where the open bracket is located is its location will provo

Concavity, derivations, and proofs

Please see attachment All the questions Determine whether....converge or diverge ...derive a necessary condition for the have a rational root. Then use this condition to prove... Using binomial coefficients, derive a formula for the nth derivative of the product of two functions. Suppose that f(x) has

Logarithmic Differentiation to find the Derivative

Use logarithmic differentiation to find the derivative f(x)= e to the 2x power (2x- 1) to the 5th power / (x to the 3rd power + 5 to the second power times (4-7x) Applied Calculus 9th edition by Laurence D Hoffman and Gerald L. Bradley

Profit Function and Maximum Profit

A manufacturer finds that the total profit from producing and selling Q units of a product is given by the profit function: Total Profit = f(Q) = - 460 + 100Q - Q^2 1. Compute the value of the function at Q=10 Total Profit = f(10)= - 460 + 100(10) - 10^2 Total Profit = f(10)= - 460

Vectors, Planes and Partial Derivatives

1. Let a = 2i + 3j and b = -9i + 6j. Find c = a - b. A) c = -3j B) c = 9i C) c = 11i + 9j D) c = 11i - 3j 2. Let a = 2i + 3j and b = -9i + 6j. Find d = a ? b. A) 36 B) -36 C) 0 D) -18i2 + 18j2 3. Find the intersection of L1: x - 2 = ½(y + 1) = 1/3(z - 3), L2: 1/3(x - 5) = ½(y - 1) = z - 4, if they

First and Second Derivatives and Minimizing

A company holds spare parts for its car maintenance service. There is a steady demand for these parts. If the company orders large numbers once a year, then they have to pay considerable warehouse costs to stock them. If they order small numbers very frequently then they have to pay considerable admin costs for processing all th

Partial Derivitives and the Chain Rule

Let F(u,v) be a function of two variables. Find f '(x) for each of the following. Use F_u and F_v for F_u and F_v (a) f(x) = F(x, 6). f '(x) = (b) f(x) = F(3, x). f '(x) = (c) f(x) = F(x, x). f '(x) =

Partial derivatives and chain rule

Find (partial z)/(partial u)( and ) (partial z)/(partial v) using the chain rule. Assume the variables are restricted to domains on which the functions are defined. Your answers should be in terms of u and v. z=arctan(x/y) x=u^2+v^2 y=u^2-v^2 partial z/partial u = Partial z/partial v =

Derivatives, Limits and Equation of Tangent Lines

1. Use the limit definition to find f'(x) for f(x) = ? (show all work). 2. Write the limit definition of derivative: f'(x) = lim 3. For the function f(x) = , use the limit definition of derivative to find the slope of the tangent line to the function at x=4. Show all steps for full credit. (b) Find the equatio

Quotient Power and Exponent Rules

Please help explain the following questions and provide an example: 1. explain the quotient rule for exponents and give an example. 2. explain the power rule for exponents and give an example. 3. explain the negative exponent rule and give an example. 4. explain the zero exponent rule and give an example.

Inflation Rate and "Rule of 70"

If the CPI was 110 last year and is 121 this year, what is this year's rate of inflation? What is the "rule of 70"? How long would it take for the price level to double if inflation persisted at (a) 2, (b) 5, and (c) 10 percent per year?

Applications of Derivatives

An isosceles triangle whose base is the interval from (0,0) to (c,0) has its vertex on the graph of f, where f(x)=12-x^2 for x is greater than or equal to 0 and f(x) is greater than or equal to 0. For what value of c does the triangle have maximum area? Justify your answer.


See attachment for equations 1) determine the interval(s) where the function is increasing and the interval(s) where it is decreasing. 2) determine the interval(s) where the function is increasing and the interval(s) where it is decreasing. 3) Find the relative maxima and relative minima, if any, of the following functi


See attached for proper formatting Rank the Critical ratio sequencing rules on the three evaluation criteria of average flow time, average number of jobs in the system, and average job lateness for the information below. (Do not evaluate shortest processing time or first-come first-served). A production planner must deci

Cowling's rule

Cowling rule is another method for determining the dosage of a drug to prescribed to a child. For this rule, the formula d=D(a+1) ------ 24 gives the child's dosage d, Where D is the adult dosage and a is the age of the child in years. If the adult dosage of a drug is 600 milligrams and a doctor uses this formula to

Applications of the Derivative

Please see the attached file for the fully formatted problems. For the function y= sq root (x2 - 9) (i) Find the slope of the tangent line to the function at the point (5, 4). (ii) Find the equation of the normal line at the point (5, 4). 2. A ladder 10 m long rests on horizontal ground and leans against a vertical wal

Market Share Analysis

This table presents units sold and market share data for the Personal Computers Industry (first figure for each company is units, second is revenue). E-Top--10,000--7,500,000 CompEZ--15,000--12,000,000 BEST--2,000--1,700,000 Moonwalk--8,000--8,000,000 CompBrain--8,000--12,000,000 Market Total--43,000 units--41,200,000

first derivative and second derivative

Please see the attached file (word problems, inflection, critical points, and derivatives) 14. You run a small furniture business. You sign a deal with a customer to deliver up to 400 chairs, the exact number to be determined by the customer later. The price will be $90 per chair up to 300 chairs, and above 300, the price wil

Application of Derivatives of Function

(See full description in the attachment). 1. With a yearly rate of 3 percent, prices are described as P = P0 (1.03)^t, where P0 is the price in dollars when t = 0 and t is time in years. If P0 is 1.2, how fast are prices rising when t = 15? 2. The value of a car is falling 10 percent per year so that if C0 is the purchase p

Managerial Finance - Ratio Analysis for Walmart and Target

Hello, Please assist me with the following study for my exam. Evaluate each firm's financial performance for the two most recent years available by (1) performing financial ratio analysis using the Microsoft® Excel® Ratio Analysis Worksheet, (2) performing trend analysis on those financial ratios. Your analysis should in

Rules of exponential function

Please see the attached file for full description. Post a response to the following: Explain three rules for exponents listed in the chart on p.239 (section 4.2). Do not explain the first two definitions listed in the table (Exponent of 1 or 0). Create an expression for your classmates to solve that uses scientific notation a

Equations for modeling

1. Given the function M(t) = 2t3 - 3t2 - 36t, find the critical values and determine, using both the second derivative test and a sign chart, the nature of these values. 2. A projectile is launched with a velocity of 22 m/s at 50° to the ground. Determine its horizontal and vertical velocities. 3. Two trains start from th