8. -/1 points details my notes scalc9 3.1.039...

# Explanation: ## Step1: Find the derivative Use the power - rule $\frac{d}{dt}(t^n)=nt^{n - 1}$. $h'(t)=\frac{3}{4}t^{\frac{3}{4}-1}-3\times\frac{1}{4}t^{\frac{1}{4}-1}=\frac{3}{4}t^{-\frac{1}{4}}-\frac{3}{4}t^{-\frac{3}{4}}=\frac{3}{4t^{\frac{1}{4}}}-\frac{3}{4t^{\frac{3}{4}}}=\frac{3t^{\frac{3}{4}}-3t^{\frac{1}{4}}}{4t^{\frac{1}{4}+\frac{3}{4}}}=\frac{3t^{\frac{1}{4}}(t^{\frac{1}{2}} - 1)}{4t}$ ## Step2: Set the derivative equal to zero $h'(t)=0$ when $3t^{\frac{1}{4}}(t^{\frac{1}{2}} - 1)=0$. Since $t^{\frac{1}{4}} = 0$ gives $t = 0$, but $h'(t)$ is undefined at $t = 0$. For $t^{\frac{1}{2}}-1=0$, we have $t^{\frac{1}{2}}=1$, so $t = 1$. Also, $h'(t)$ is undefined when $t=0$ (because of the negative - exponents in the derivative). # Answer: 0,1