f(x) from the graph f '(x)

1. f(x) is increasing at -2When the output is of the graph f,(x) is positive the function f(x) is increasing when the output for the graph of f'(x) is negative he function f(x) is decreasing when the output for the graph is zero it means f(x) is not decreasing or increasing it is just at rest therefore the intervals in which f(x) is increasing those not include -2, 0, and 2
2. The extremas are at x=-2 and 2
at x=-2 there is a local min. and at x=2 there is a local max
at x=-2 in the graph f'(x) the output is zero from the left of x=-2 it is negative and from the right it is positive therefore making it minimum. At x=2 the output is zero, from the left of x=2 it is positive and from the right it is negative making it a maximum
3. its concaved up at (-infinity , -3/2) U (0, 1)
its concaved down at (-3/2, 0)U (1, positive infinity)
Since the graph shows f'(x) taking the derivative (in otherwords the slope) of f'(x) will give you f''(x). When f''(x) is positive it is concaved up when f''(x) is negative it is concaved down
4.f(x)could equal to x^5. f'(x) is x^4 when using the antiderivative of f'(x)=x^4 and f(x) should be x^5.