Determine, using the graph of the function, the intervals on which f(x) = 9 − x^2 is increasing and the intervals on which it is decreasing. (Enter your answers using interval notation.)

Question

I have the answer, I just need the interval notation explained/shown.

Answer 1

f(x) =9-x^2 is a downward opening parabola

with vertex = maximum = (0,9)

the function is increasing to the left of the vertex and decreasing to the right

decreasing in the interval (0,infinity)

increasing in the interval (-infinity, 0)

f(x) is increasing when f'(x)>0 and decreasing when f'(x)<0

f'(x)=-2x < 0 when x>0

and f'(x)>0 when x<0