Question

Find all local maxima and minima and values of x were they occur. f(x)=(x+3)(x-1)^2
(Round to two decimal places)

Answer 1

f(x)=(x+3)(x-1)(x-1)
f(x)-x^2+2x-3(x-1)
f(x)=x^3+x^2-5x+3
to find the local max and min you need to take the derivative and set that = 0
f'(x)=3x^2+2x-5=0
(3x+5)(x-1)=0
x=-5/3
x=1
now plug those into your original eq
f(x)=(x+3)(x-1)(x-1)
testing x=-5/3
f(-5/3)=(-5/3+3)(-5/3-1)^2
f(-5/3)=4/3(-8/3)^2
f(-5/3)=4/3(64/9)
f(-5/3)=256/27=9.48
now test x=1
x=1 the function is 0 because (x-1) plug x=1 its 0
so you have a max at (-5/3,9.48) and a min at (1,0)