Question

Sorry for all of the questions..

if f'(x) exists for all x and f(-1)=-12 and f(5)=12, then for at least one value of c where -1<c<5, what must be true?
a) f'(c)=4
b) f'(c)=-4
c)f(c)=14
d)f(c)=-14
e) f'(c^2)=64

Answer 1

the slope of the line from (-1,-12) to (5,12) = 4, so think of the Mean Value Theorem.