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Partial derivative

See attachment Compute the first partial derivatives of the function: W = 4x^3 y^2 - 3xyz + 7yz^2

Chain Rule

The radius of a right circular cone is increasing at a rate of 1.6in/s while its height is decreasing at a rate of 2.5 in/s. At what rate is the volume of the cone changing when the radius is 120in and the height is 140in?


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

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

Derivatives and inflation

With a yearly inflation rate of 7%, prices are given by P=p(1.05)^t, where p is the price in dollars when t=0 and t is the time in years. Suppose p=1. How fast (in cents/ year) are prices rising when t=12? Find f'(x) and f''(x) if f(x)=(4x^2+12)(3x-1)


Find the derivative of w(x)=tan(x^4) Find dy/dx of (the square root of x + square root of y)=36


Let xy^2+2y(x+2)^2+2=0 a) if x changes from -2.00 to -2.01 and y>0, approximately how much does y change? b)if x changes from -2.00 to -2.01 and y<0, approximately how much does y change?


Find the value of c in Figure 3.12 (picture attached), where the line l tangent to the graph of y = 2x at (0, 1) intersects the x-axis. Give your answer correct to 2 decimal places. Find the derivative of the function below. f(x) = e^2 + x^e

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

Partial Derivatives

Each function f is homogeneous of degree n, that is f satisfies the equation f(tx,ty)= t^n f(x,y) for all t, where n is a positive integer and f has continuous second-order partial derivatives. Verify that f satisfies the given equation see attached page for equation

Find rate of change

The temperature T in a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (1,2,2) is 120 degrees. Find the rate of change of T at (1,2,2) in the direction toward the point (2,1,3) Show that at any point in the ball the direction of

Solving differential equations

Please help with these problems regarding integrals and differentiation: section 2.2 # 10,18,22,26,30,38 (attached images) thanks

Trapezoidal Rule

Let L(x) = int(1/t, t=1..x) for all x>0. a) Find L(1). b) Find L'(x) and L'(1). c) Use the Trapezoidal Rule to approximate the value of x (to three decimal places) for which L(x) = 1. d) Prove that L(x1 * x2) = L(x1) + L(x2), for x1 > 0 and x2 > 0. [Obs: My CAS is Maple]

Differential Calculus

See attached. The (n-1)-dimensional sphere can be realized as the zero set of the function.....


Please see attachment Find the derivatives of the given functions... Find the equations of all lines through the origin tangent to the parabola...

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

Draw the function

1. Draw in a surrounding of O the graph of the following function: f(x) = -1 + 3x - (3x)2 + (3x)3 - (3x)4 + ........ showing the value in O of the derivative first, second, and tenth. (see attached)

Rate of change and derivatives

(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

Drag and velocity

See attached A parachutist falling to earth is subject to two forces...