Identify $\frac{dy}{dx}$ for the following using implicit differentiation:

$2y^2 + 2x^2 = 4$

Identify $\frac{dy}{dt}$ for the following:

$2y = 3x^3 + \cos(x)$

Identify the critical points of the following. (Only identify the $x$-values):

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

Identify the critical points of the following. (Only identify the $x$-values of the points):

$f(x) = \ln(x^2) + 3$

Identify all extrema for the function below. Note that relative extrema are excluding any absolute extrema:

$f(x) = x^3 − 3x^2 + 2$

Identify all extrema for the function below. Note that relative extrema are excluding any absolute extrema.

$f(x) = \ln(x^2)$

Let the graph below represent the first derivative of the function $f(x)$. Identify the $x$-values for all extrema of $f(x)$. Note that relative extrema is excluding any absolute extrema.

Identify the 2^nd derivative of the function below:

$f(x) = \sin^3(3x)$

Identify the 5^thderivative of the function below:

$f(x) = \ln(2x)$

Identify any points of inflection for the function below:

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

Identify the points of inflection for the function below:

$f(x) = e^{3x^2 + 2}$

Identify where the function below is concave up:

$f(x) = 6x^3 + 3x^2 + 2x$

Identify where the following function is concave down on the given domain:

$f(x) = \sin(3x), −\frac{π}{3} ≤ x ≤ \frac{π}{3}$

Identify where the function $f(x)$ is concave up and concave down given the graph of the second derivative below.

Identify the concavity and the points of inflection for the function $f(x)$ given graph of the first derivative of the function, $f'(x)$, below.