a. For the function f(x) = 4x2 + 11x, find the value of

Chapter 3, Problem 48E

(choose chapter or problem)

Problem 48E

a. For the function f(x) = −4x2 + 11x, find the value of f′(3), as well as the approximation using

and using the formula in with h = 0.1.

b. Repeat part a using h = 0.01.

c. Repeat part a using the function f(x) = −2/x and h = 0.1.

d. Repeat part c using h = 0.01.

e. Repeat part a using the function  and h = 0.1.

f. Repeat part e using h = 0.01.

g. Using the results of parts a through f, discuss which approximation formula seems to give better accuracy.

Exercise

Explain why

should give a reasonable approximation of f′(x) when f′(x) exists and h is small.