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Derivatives

Derivatives and Tangent Lines

3. Answer these questions. a. Find f'(x) where f(x)= 3x4 + 2 - b. Find the equation of the tangent line at x=1 for the function f(x) from part a. c. Find for y=2lnx+5x -2log3x

Derivatives and Extrema

For the function f(x)=(x)/(x^2+9) a) Find f'(x) using the appropriate rule and simplify to one expression with positive exponents. b) Find all values of x, using algebra, where f'(x)=0 (Write your answer with positive exponents) *** I could really use some help on this one. Thanks :)

Avg. Rate of Change /Find Derivative /Instant Rate of Change

For the function f(x)=(3x)/(x+2) a. find the average rate of change from x=2 to x=5 b. find the derivative f'(x) from first principles, by setting up the difference quotient, (f(x+h)-f(x))/(h) and finding lim h->0 (f(x+h)-f(x))/(h) c. use part b to find the rate of change of f(x) at x=2

Definition of the Derivative

Specifically, I want you to calculate each derivative using our limit formula: and 1. f(x) = 7 2. 3. 4. 5. 6. Assume and . Calculate the derivative of [ ].

Mean Value Theorem : Roots of Derivatives on an Interval

The function f (x) and all of its derivatives are continuous on [0, 10]. You know that f (0) = 0, f (2) = 0, f (3) = 0, f (6) = 0, and f (8) = 0. At how many points must the first derivative of f (x) be zero? At how many points must the second derivative of f (x) be zero? At how many points must the third derivative of f (x) b

Slope predictor function, derivative, maximization

Given f( x) = 2/x-1 , use the four step process to find a slope predictor function m(x). Then write an equation for the line tangent to the curve at the point x = 0. Find f'(x) given f (x) = 5x^3- 4x^2+ 3x- 2 / X^2 . A farmer has 480 meters of fencing. He wishes to enclose a rectangular plot of land and to divide

Derivatives and tangents

Use the definition of the derivative to find f '(x) given f(x)=^/¯x Write an equation of the line tangent to the curve at the point P(-1, 7). Express the answer in the form ax + by = c. y= 5/x^2-2/x^3 Write the equation of the line tangent to the curve at the point P where x = 4. Write the equation in the f

Minimizing Surface Area

A container company is going to construct a shipping container of volume 12 ft3 with a square bottom and a square top. The cost of the top and sides is $2 per square foot and for the bottom is $3 per square foot. What dimensions will minimize the cost of the container.

Fifth Derivative

Compute the fifth derivative of 1 / g(x). You can use Faa di Brunos formula if you wish.

Maximum and Minimum Values of Functions

The Association of Economists Least Likely to Win Any Awards (AELLWAA) was founded 20 years ago.... Find the maximum and minimum years of membership for the attached equation.

minimizing the average cost

A domestic auto producer is facing intense competition in the US market from Asian imports. The CFO decides that the solution is to produce at the point at which average cost is minimized, i.e. where TC/Q is at a minimum. The firm's cost structure is given by: TC={(1/3Q)^3}-{(100Q)^2}+20,000Q Calculate the average cost-min

Antiderivatives

? Guess an antiderivative of and verify by differentiation that your guess is correct. ? Guess an antiderivative of and verify by differentiation that your guess is correct. ? Guess an antiderivative of and verify by differentiation that your guess is correct. ? Guess an antiderivative of and verify by differentiat

Solve: Decreasing Functions

Determine the intervals on which the function is increasing and intervals on which the function is decreasing. Check your answers by graphing the corresponding functions. - Please view the attachment for the rest of the solution.

Differentiability and Derivatives

Please see the attached file for the fully formatted problems. 1. Let be a positive number and defined by Determine all values of k such that f is differentiable at 0. What is f' (0) then?

Derivatives and Extreme Values

1. Find the maximum and minimum values of defined on the interval . 2. Find the maximum and minimum values of defined on the interval . 3. Find the maximum and minimum values of on the interval . Then graph the function to check your answers. Please see the attached file for the fully formatted problems.

Solve: Derivatives, Chain Rule and Rate of Change

Please assist me with understanding the following questions: 1. A glider is flying along the line y = - (1/3)x + 100. Its horizontal shadow is moving at 10 m/s. How fast is the glider approaching the origin (0,0) at the time when it is located at (-30, 110)? 2. Boyle's Law states that when a sample of gas is compressed a

Definition of the Derivative & Questions

Please see the attached file for the fully formatted problems. The first page is explanation of the derivative as it is in my class and the second holds the questions I require assistance with.

Description of Cramer's rule

Solve the following linear system for x using Cramer's rule. Show work. x + 2y - 3z = -22 2x - 6y + 8z = 74 -x - 2y + 4z = 29

Local Extrema and Volume of a Solid of Revolution

Please see attached file for full problem description. The graph of the derivative of a function f is shown below. (a) Over what intervals is f(x) increasing? decreasing? Why? (b) At what x values does f(x) have a local maximum? Why? (c) At what x values does f(x) have a local minimum? Why? (d) Sketch a possible

Partial Differentiation

Text Book : Advance Calculus, Author: - Taylor and Menon In page number 160 I need following questions following questions to be answered: 2, 4, 7 & 11. Please mention each and every step.

Finding the first and second derivative.

Y= (1 + 1/x)^1/4 Got the 1st derivative to be Y'= 1/4 (1+1/x)^-3/4 * (-1x)^-2 Is that correct? Now I need the 2nd derivative, I am completely lost on this. Please work out clearly.