\( \int _{}^{}\frac{dx}{x^{2}-8x-16} d \)

Find an equation of the line tangent to the given curve at \( \mathrm{x}=\mathrm{a} \). \[ y=4+6 x+11 x e^{x} ; a=0 \] The equation for the tangent line is \( y=\square \).

Determine the interval(s) on which the following function is continuous. \( f(x)=\frac{x^{2}-8 x+15}{x^{2}-9} \) The function is continuous on the interval(s) (Simplify your answer. Type your answer in interval notation. Use a comma to sepa

Suppose that \( f(x, y)=x^{4}+y^{4}-x y \). Then the minimum value of \( f(x, y) \) is.. A. -0.125 B. 0.125 C. 0 D. None of these answers

Let \( f(x)=2 x^{3}+3 x^{2}-12 x+1 \). a. Find all points on the graph of \( f(x) \) at which the tangent line is horizontal. b. Find all points on the graph of \( f(x) \) at which the tangent line has slope 108 .

Find the derivative of the following function. \( g(t)=4 \sqrt{t} \) \( g^{\prime}(t)=\square \)