h(t)=t34−3t14
Note that the domain of h is [0,∞].
By differentiating,
h'(t)=34t−14−34t−34
by factoring out 34,
=34(1t14−1t34)
by finding the common denominator,
=34t12−1t34=0
⇒t12=1⇒t=1
Since h'(0) is undefined, t=0 is also a critical number.
Hence, the critical numbers are t=0,1.
I hope that this was helpful.
