Determine whether the following statements are true and give an explanation or counterexample. Assume f and f' are continuous functions for all real numbers. 

a. If then A is a quadratic function.

b. Given an area function and an antiderivative F of f , it follows that A'(x) = F(x).

c.

d. If f is continuous on [a, b] and  then f(x) = 0 on [a, b].

e. If the average value of f on [a, b] is zero, then f(x) = 0 on [a, b].

f.

g.

Transcribed Image Text:

A(x) = J"f(t) dt and f(t) = 2t – 3, A(x) = [,f(t) dt f(t) dt