(10 points) Use the Fundamental Theorem of Calculus to find the exact values of the definite integral. \( \int_{1}^{3} 3\left(2^{x}\right) d x= \)

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

Find the derivative of the following function by first expanding the expression. \[ f(x)=(6 x+1)\left(5 x^{2}+7\right) \] \( f^{\prime}(x)=\square \)

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

Given \( f(x, y)=3 x^{3}+x y^{2}-2 y^{6} \), find \( f_{y} \) \( 2 x-60 y \) \( 18 x \) \( 2 y \) None of these answers

Find the intervals on which \( f \) is increasing and the intervals on which it is decreasing. \( f(x)=\frac{x^{4}}{4}-3 x^{3}+9 x^{2} \)