Question

OH, I forgot to post this one with my last two questions! Here it is:

3. f is a differentiable function for all x. Which of the following statements must be true?

I- the derivative with respect to x of the integral from 0 to 4 of f of x, dx is equal to f of x
II- d dx of integral from x to 4 of f of t d t equals negative f of x
III- the integral from 4 to x of f prime of x, dx is equal to negative f of x

A. II only
B. III only
C. I and II only
D. II and III only

THANK YOU!

Answer 1

#3 II only. Check the FTC
I is false because ∫[0,4] f(x) dx is just a number
III is false because ∫[4,x] f'(x) dx = f(x)-f(4)