91Ó°ÊÓ

The daily temperature in degrees Fahrenheit of Phoenix in the summer can be modeled by the function \(T(x)=94-10 \cos \left[\frac{\pi}{12}(x-2)\right],\) where \(x\) is hours after midnight. Find the rate at which the temperature is changing at 4 p.m.

The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled by the function \(D(t)=5 \sin \left(\frac{\pi}{6} t-\frac{7 \pi}{6}\right)+8,\) where \(t\) is the number of hours after midnight. Find the rate at which the depth is changing at 6 a.m.

[T] The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled by the function \(D(t)=5 \sin \left(\frac{\pi}{6} t-\frac{7 \pi}{6}\right)+8, \quad\) where \(t\) is the number of hours after midnight. Find the rate at which the depth is changing at 6 \(\mathrm{a.m.}\)

Use the functions \(y=f(x)\) to find a. \(\frac{d f}{d x}\) at \(x=a\) and b. \(\quad x=f^{-1}(y)\) c. Then use part b. to find \(\frac{d f^{-1}}{d y}\) at \(y=f(a)\). $$ f(x)=6 x-1, x=-2 $$

For the following exercises, use the functions \(y=f(x)\) to find a. \(\frac{d f}{d x}\) at \(x=a\) and b. \(x=f^{-1}(y).\) c. Then use part b. to find \(\frac{d f^{-1}}{d y}\) at \(y=f(a).\) $$f(x)=6 x-1, x=-2$$

Use the functions \(y=f(x)\) to find a. \(\frac{d f}{d x}\) at \(x=a\) and b. \(\quad x=f^{-1}(y)\) c. Then use part b. to find \(\frac{d f^{-1}}{d y}\) at \(y=f(a)\). $$ f(x)=2 x^{3}-3, x=1 $$

For the following exercises, use the functions \(y=f(x)\) to find a. \(\frac{d f}{d x}\) at \(x=a\) and b. \(x=f^{-1}(y).\) c. Then use part b. to find \(\frac{d f^{-1}}{d y}\) at \(y=f(a).\) $$f(x)=2 x^{3}-3, x=1$$

Use the functions \(y=f(x)\) to find a. \(\frac{d f}{d x}\) at \(x=a\) and b. \(\quad x=f^{-1}(y)\) c. Then use part b. to find \(\frac{d f^{-1}}{d y}\) at \(y=f(a)\). $$ f(x)=9-x^{2}, 0 \leq x \leq 3, x=2 $$

For the following exercises, use the functions \(y=f(x)\) to find a. \(\frac{d f}{d x}\) at \(x=a\) and b. \(x=f^{-1}(y).\) c. Then use part b. to find \(\frac{d f^{-1}}{d y}\) at \(y=f(a).\) $$f(x)=9-x^{2}, 0 \leq x \leq 3, x=2$$

For the following exercises, use the functions \(y=f(x)\) to find a. \(\frac{d f}{d x}\) at \(x=a\) and b. \(x=f^{-1}(y).\) c. Then use part b. to find \(\frac{d f^{-1}}{d y}\) at \(y=f(a).\) $$f(x)=\sin x, x=0$$