1. For the function f(x)=4x^3-30x^2+4:

Question

a) Find the critical numbers of f(if any);
b) Find the open intervals where the function is increasing or decreasing; and
c) Apply the First Derivative Test to identify all relative extrema
2. For the function f(x)=(x-1)^(8/11)
a) Find the critical numbers of f(if any);
b) Find the open intervals where the function is increasing or decreasing; and
c) Apply the First Derivative Test to identify all relative extrema

Answer 1

f' = 12x^2 - 60x = 12x(x-5)

as you know
extrema where f'=0
increasing where f' > 0