Please help with D Free ResponseThe table below represents values of differentiable functions, f and g, and their first derivatives.Use the table of values to answer the questions that follow.f(x)f'(x)g(x)g'(x)-38-4-2-221-22-32-42-4-6A. Is there a value of r on -3 < r < 2 such that f (r) = 0 ? Give a reason for your answer.B. Approximate the value of g"(1.5). What does this value say about the graph of g when x = 1.5?C. If h(x) = [f (x)]² + g(x), what is the equation of the line tangent to the graph of h at x = -2?D. Is there guaranteed to exist a value of x = c on –2 < c < 2, such that h' (c) = 0? Give a reason foryour answer.3.3.3.

Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and…

Answered: D. Is there guaranteed to exist a value…

Math

Calculus

D. Is there guaranteed to exist a value of x = c on -2 < c < 2, such that h'(c) = 0? Give a reason for your answer.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

ChapterP: Prerequisites

Section: Chapter Questions

Problem 8PS

See similar textbooks

Similar questions

Hollings Functional Response Curve The total number P of prey taken by a predator depends on the availability of prey. C.S. Holling proposed a function of the form P=cn(1+dn) to model the number of prey taken in certain situations. Here n is the density of prey available, and c and d are constants that depend on the organisms involved as well as on other environmental features. Holling took data gathered earlier by T. Burnett on the number of sawfly cocoons found by a small wasp parasite at given host density. In one such experiment conducted, Holling found the relationship p=21.96n1+2.41n, Where P is the number of cocoons parasitized and n is the density of cocoons available measured as number per square inch. a Draw a graph of p versus n. Include values of n up to 2 cocoons per square inch. b What density of cocoons will ensure that the wasp will find and parasitize 6 of them? c There is a limit to the number of cocoons that the wasp is able to parasitize no matter how readily available the prey may be. What is this upper limit?
Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.
Maximum Sales Growth This is a continuation of Exercise 10. In this exercise, we determine how the sales level that gives the maximum growth rate is related to the limit on sales. Assume, as above, that the constant of proportionality is 0.3, but now suppose that sales grow to a level of 4 thousand dollars in the limit. a. Write an equation that shows the proportionality relation for G. b. On the basis of the equation from part a, make a graph of G as a function of s. c. At what sales level is the growth rate as large as possible? d. Replace the limit of 4 thousand dollars with another number, and find at what sales level the growth rate is as large as possible. What is the relationship between the limit and the sales level that gives the largest growth rate? Does this relationship change if the proportionality constant is changed? e. Use your answers in part d to explain how to determine the limit if we are given sales data showing the sales up to a point where the growth rate begins to decrease.
Average Rate of change A fucntion f is given. (a) Find the average rate of change of f between x=0 and x=0 , and the average rate of change of f between x=15 and x=50 .(b) Were the two average rates of change that you found in part (a) the same? (c) Is the function linear? If so, what is its rate of change? f(x)=83x
Average Rate of change A fucntion f is given. (a) Find the average rate of change of f between x=0 and x=0 ,and the average rate of change of f between x=15 and x=50 . (b) Were the two average rates of change that you found in part (a) the same? (c) Is the function linear? If so, what is its rate of change? f(x)=12x6