Given a graph of f'(x). At which value of x does f(x) have a maximum?

Question

Given a graph of f'(x). At which value of x does f(x) have a maximum at which the points are (-4,0), (-2,-6), (-1,0) and (0,2)?

a) -4

b) 0

c) -1

d) -2

Answer 1

The graph of f'(x) shows the slope of the graph f(x) for each value of x. Since the f'(x) graph have points at (-4,0) and (-1,0), that means that the slope of f(x) and x = -4 and -1 is zero, which means there is either a maximum or minimum at these locations.

We know that at a minimum for an f(x) graph, the slope changes from negative to positive. Visa versa, we know that at a maximum for an f(x) graph, the slope changes from positive to negative. This means that in order to find the maximum of f(x), we need to find the point where the y value changes from positive to negative. At point (-1,0), the y value changes from -6 to 2, which shows this point is a minimum. Therefore, x = -4 is a positive.

a) -4