Exam 4: Applications of the Derivative

Solve the problem. -Select an appropriate graph of a twice-differentiable function y = f(x) that passes through the points and whose first two derivatives have the following sign patterns.

Choose the one alternative that best completes the statement or answers the question. -Suppose a business can sell x gadgets for p = 250 - 0.01x dollars apiece, and it costs the business dollars to produce the x gadgets. Determine the production level and cost per gadget required to maximize profit.

Graph the equation. Include the coordinates of any local extreme points and inflection points. -y = x^1/3(x² - 63)

Use Newton's method to approximate all the intersection points of the pair of curves. Some preliminary graphing or analysis may help in choosing good initial approximations. Round to six decimal places. -y = and y = + 3

Find the absolute extreme values of the function on the interval. -f(x) = - 6 , - $\infty$ < x < $\infty$

Solve the problem. -Given the velocity and initial position of a body moving along a coordinate line at time t, find the body's position at time t. v = -7t + 3, s(0) = 12

Use l'Hopital's Rule to evaluate the limit. -

Use l'Hopital's Rule to evaluate the limit. -