AP Calculus AB Easy practice

A function $f$ is continuous on $[-3,5]$. Which theorem guarantees that $f$ attains both a maximum and a minimum value on this interval?

Find the area enclosed between $y=x$ and $y=x^2$ on $[0,1]$.

Solve the separable ODE $\frac{dy}{dx}=\frac{x}{y}$ with $y(0)=4$. (Give the solution for $y>0$.)

If the position of a particle is $s(t)=t^3-6t^2+9t$ (in meters, $t$ in seconds), what is its velocity at $t=2$?

Evaluate ${\int }_0^2(x^2+1)dx$.

A particle moves along a number line so that its position is $s(t)=t^3-6t+2$ (feet, $t$ in seconds). What is the velocity at $t=2$?

Find the equation of the tangent line to $f(x)=x^2$ at $x=3$.

Evaluate $\int (3x^2+4x-5)dx$.

Differentiate $y=\ln (x^4+7)$ with respect to $x$.

Find the derivative of $f(x)=5x^3-4x^2+7x-2$.

Which of the following is the solution to $\frac{dy}{dx}=2x$ with initial condition $y(0)=3$?

If $y=\arctan (2x)$, what is $\frac{dy}{dx}$?

If $f$ is differentiable at $x=a$, then $f$ is:

Evaluate $\underset{x\to 0}{\lim }\frac{\sin (3x)}{x}$.

If $f(x)=x\sin x$, find $f^{\prime }(x)$.