Calculus 1

Use implicit differentiation to find $\frac{dy}{dx}$ for the following equation

$x^2 + y^2 = 25 + 5x$

For the following function, find $\frac{dy}{dx}$ by implicit differentiation

$x^2 + 2xy + y^2 = 5$

Find the derivative of the following hyperbolic function

$f(x) = \sin{(\sinh{(x)})}$

Find and classify the critical points of the following function

$f(x) = x^3 - 3x^2 - 9x + 2$

Find the inflection points and intervals of concavity for the following function

$y = \frac{x^2 + 1}{x^2}$

Find two non-negative numbers, x and y, whose sum is 9 with a maximum product of x and the square of y, $p(x,y) = xy^2$

A man has 1000 feet of fencing material and he wants to enclose three adjacent pens for his three dogs as shown below. What dimensions should be used to maximize the total enclosed area? What is the final maximum total area?

Determine the volume of the solid generated by rotating the function about the y-axis on $[0,4]$

$y = \sqrt{x}$