Consider the function \( g(x)=(x-4)^{\frac{2}{3}} \). a. Find the critical points of \( g(x) \). (Enter as a comma-separated list, or enter DNE for "does not exist" if there are none.) 4 b. Find the absolute extrema of \( g \) on the interval \( [0,11] \). Enter only the function values. The absolute maximum is: The absolute minimum is: 0

Given the scalar fild \[ f(x, y, z)=x^{2}+y^{3}+z^{2}+1 \] compute the Iaplacion \( \vec{\nabla}^{2} f=\frac{\partial^{2} f}{\partial x^{2}}+\frac{\partial^{2} f}{\partial y^{2}}+\frac{\partial^{2} f}{\partial z^{2}} \)

Solve the rational inequality. Write your answer in interval notation. \( \frac{(x+12)(x-4)}{x-1} \geq 0 \)

A stunt car traveling at \( 20 \mathrm{~m} / \mathrm{s} \) flies horizontally off a cliff and lands 39.2 m from the base of the cliff. How tall is the cliff?

Solve the following rational inequality \( \frac{x-3}{x^{2}-64}>0 \) State your answer using interval notation. Use U for union and oo for \( \infty \).

Solve the following equation. \[ \log _{\mathrm{x}} 3^{12}=24 \] Rewrite the equation in exponential form.