Consider the following function.

Question

Find the critical numbers of f. (Enter your answers as a comma-separated list.)

f(x) = (5 − x)(x + 1)²

X=

Answer 1

f(x) = (5-x)(x+1)^2

f(x) = -x^3 +3x^2 + 9x +5

f'(x) = -3x^2 +6x +9

f'(x) = (x-3)(x+1) = 0

x =-1 and 3

(-1,-6) is a relative or local minimum

(3,32) is a relative or local maximum

there's also an inflection point between them midway from x=-1 to x=3

where 2nd derivative = f"(x)=0 = -6x+6

x=1, y= 16, (1,16) where concavity changes