Calculus Question

Question

use the following partial graph of a polynomial function, with a local maximum at x = -4 and a local minimum at x =2 to answer the following question.

B) State whether f'(-3.9) and f'(-4.1) are positive or negative.

Help!?

Answer 1

f(x) has a local maximum at x = -4.  That means that f(x) is increasing in the interval prior to x=-4 and decreasing after it.  Remember, f(x) is the slope of the line tangent to f(x) at x.  So f'(x) is positive where the function is increasing and negative where it's decreasing.