Question

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
h(t) = t3/4 − 3t1/4

Answer 1

H(t) = t^(3/4) - 3t^(1/4)

The critical points can be evaluated by taking the first derivative and equating to 0.

h'(t) = 3 / t^(1/4)  - 3 / 4t^(3/4)
3 / (4t^(3/4)) = 3 / t^(1/4)
4t^(3/4) = t^(1/4)

4 = 1/√t
t = 1/16, t = -1/16