Anyone want to choose the answer which best describes those statements.?

Question

A: The derivative of a definite integral is always zero.
B: If f(x) = |2x - a| , then f '(2a) does not exist.
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a. Only A is true.
b. Only B is true.
c. Both A and B are true.
d. Both A and B are false.

Answer 1

B is false: Let a be any number other than zero. If a>0, 2(2a)-a > 0, and f'(2a) = 2. Conversely, if a<0, 2(2a)-a<0, and f'(2a) = -2. Thus, any value of a other than zero serves as a counterexample.

A is also false, although I'm not sure your teacher knows this. She may be thinking of something like f(x)=[a, b]∫g(t) dt, which is alawys a constant function regardless of g(t), and thus its derivative is zero. However, if the free variable appears in the limits of integration, the function may be nonconstant: for instance, let f(x) = [1, x]∫1/t dt, which is equal to ln x for positive values of x, and its derivative is certainly not zero. So the correct answer here is d: both A and B are false.

Answer 2

I think that some people are reluctant to just do your homework; I know that I am. It hurts more than helps you.