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Numerade Educator

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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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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.