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Problem 37 Medium Difficulty
Find the critical numbers of the function
$ h(t) = t^\frac{3}{4} - 2t^\frac{1}{4} $
Answer
$$h(t)=t^{3 / 4}-2 t^{1 / 4} \Rightarrow h^{\prime}(t)=\frac{3}{4} t^{-1 / 4}-\frac{2}{4} t^{-3 / 4}=\frac{1}{4} t^{-3 / 4}\left(3 t^{1 / 2}-2\right)=\frac{3 \sqrt{t}-2}{4 \sqrt[4]{t^{3}}}$$ $$h^{\prime}(t)=0 \Rightarrow 3 \sqrt{t}=2 \Rightarrow \sqrt{t}=\frac{2}{3} \Rightarrow t=\frac{4}{9} \cdot h^{\prime}(t)$$
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Top Calculus 2 / BC Educators
Anna Marie V.
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Watch More Solved Questions in Chapter 4
Video Transcript
use the power rule to take the derivative minus two times 1/4 teach the night of three over four. And we know we can simplify this to write as three squared of teams, too over four. Cheat the 3/4. And now that we have this, we know that we can set zero equals three squirt of two minus t was like a three squirt of T minus two. So for tea and we end up with T equals 2/3 squares, that's 4/9 and then remember that zero is also a critical number.
Top Calculus 2 / BC Educators
Anna Marie V.
Campbell University
Kayleah T.
Harvey Mudd College
Samuel H.
University of Nottingham
Michael J.
Idaho State University