Evaulate the function at the indicated values h(t)=t+(3/t)i find h(x-1)

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.

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