Answer:Since the 90% is 63.
Step-by-step explanation:
Answer:
Step-by-step explanation:
your right on 105 cubic feet
![\bf f(x)=\cfrac{x}{x^2+2}\implies \cfrac{dy}{dx}=\cfrac{1(x^2+2)-(x)(2x)}{(x^2+2)^2}\\\\\\ \cfrac{dy}{dx}=\cfrac{x^2+2-2x^2}{(x^2+2)^2} \\\\\\ \cfrac{dy}{dx}=\cfrac{2-x^2}{(x^2+2)^2}\implies 0=2-x^2\implies x=\pm\sqrt{2} \\\\\\ \textit{now }-\sqrt{2}\textit{ is outside the range of }[0,4],\textit{ so is only }\sqrt{2}](https://tex.z-dn.net/?f=%5Cbf%20f%28x%29%3D%5Ccfrac%7Bx%7D%7Bx%5E2%2B2%7D%5Cimplies%20%5Ccfrac%7Bdy%7D%7Bdx%7D%3D%5Ccfrac%7B1%28x%5E2%2B2%29-%28x%29%282x%29%7D%7B%28x%5E2%2B2%29%5E2%7D%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7Bdy%7D%7Bdx%7D%3D%5Ccfrac%7Bx%5E2%2B2-2x%5E2%7D%7B%28x%5E2%2B2%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7Bdy%7D%7Bdx%7D%3D%5Ccfrac%7B2-x%5E2%7D%7B%28x%5E2%2B2%29%5E2%7D%5Cimplies%200%3D2-x%5E2%5Cimplies%20x%3D%5Cpm%5Csqrt%7B2%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ctextit%7Bnow%20%7D-%5Csqrt%7B2%7D%5Ctextit%7B%20is%20outside%20the%20range%20of%20%7D%5B0%2C4%5D%2C%5Ctextit%7B%20so%20is%20only%20%7D%5Csqrt%7B2%7D)
the denominator yields no critical points, so is only that one, which IS within the range of [0, 4].
f(0) = 0 and f(4) is about 0.2222... whilst f(√2) is about 0.3536
now, doing a first-derivative test, the √2 points is a maximum, and and the 0 and 4 are both minima, from which the 0 is lowest than the 4, notice f(0) = 0 and f(4) is up above that.
so the absolute minimum is f(0), and the absolute maximum is f(√2).