Critical Values, Partition Numbers, and the Increasing/Decreasing Test

Question

Let f(t)= 5t^2/3+ t^2/3

a) Find all partition numbers of f(t) and list them

b) Find all critical values of f(t) and list them

c) Find the interval where f(t) is increasing

d) Find the interval where f(t) is decreasing

Answer 1

f(t) = 5t^(2/3) + t^(2/3) = 6t^(2/3)

f'(t) = 4/t(1/3) > 0 when t>0

f'(t) <0 when t<0

f'(t) is undefined when t=0

interval when f(x) is increasing is (0, infinity)

interval when f(x) is decreasng is (-infinity, 0)

critical point is the origin, (0,0)