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shusha [124]
3 years ago
10

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

Mathematics
1 answer:
alex41 [277]3 years ago
6 0

<span>h<span>(t)</span>=<span>t<span>34</span></span>−3<span>t<span>14</span></span></span>

Note that the domain of h is <span>[0,∞]</span>.

By differentiating,

<span>h'<span>(t)</span>=<span>34</span><span>t<span>−<span>14</span></span></span>−<span>34</span><span>t<span>−<span>34</span></span></span></span>

by factoring out <span>34</span>,

<span>=<span>34</span><span>(<span>1<span>t<span>14</span></span></span>−<span>1<span>t<span>34</span></span></span>)</span></span>

by finding the common denominator,

<span>=<span>34</span><span><span><span>t<span>12</span></span>−1</span><span>t<span>34</span></span></span>=0</span>

<span>⇒<span>t<span>12</span></span>=1⇒t=1</span>

Since <span>h'<span>(0)</span></span> is undefined, <span>t=0</span> is also a critical number.

Hence, the critical numbers are <span>t=0,1</span>.

I hope that this was helpful.

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