Find the equation of the line tangent to $f(x)=3x^2+2x$ at $x=-5$.

Find the average rate of change of $u(x)=x^2+8x+5$ on the interval $\left[-2,0\right]$.

Find the equation of the line normal to $q(x)=-4x^2-6x$ at the point $\left(-6,-108\right)$.

Simplify the difference quotient $\frac{r(x+h)-r(x)}{h}$ for $r(x)=-9x-2$, where $h\ne 0$.

The distance covered by a train after $t$ hours is $D(t)=2t^2+3t$ kilometers, and $D^{\prime }(t)=4t+3$. What is the instantaneous rate of change at $t=3$?

Find the equation of the line normal to $p(x)=2x^2-9x$ at the point $\left(-2,26\right)$.

Find the average rate of change of $v(x)=-2x^2-6x+1$ on the interval $\left[-4,2\right]$.

At what value of $x$ is $f(x)=\left|4x-8\right|$ not differentiable, and why?

Use the definition $u^{\prime }(x)={\lim }_{h\to 0}\frac{u(x+h)-u(x)}{h}$ to find $u^{\prime }(x)$ for $u(x)=-x^2-2x+8$.

The distance covered by a train after $t$ hours is $D(t)=4t^2+7t$ kilometers, and $D^{\prime }(t)=8t+7$. What is the instantaneous rate of change at $t=3$?

Simplify the difference quotient $\frac{u(x+h)-u(x)}{h}$ for $u(x)=4x-9$, where $h\ne 0$.

Find the equation of the line tangent to $v(x)=-4x^2-3x$ at $x=-1$.

Use the definition $w^{\prime }(x)={\lim }_{h\to 0}\frac{w(x+h)-w(x)}{h}$ to find $w^{\prime }(x)$ for $w(x)=-6x^2+7x-9$.

At what value of $x$ is $f(x)={\left(x+4\right)}^{2/3}$ not differentiable, and why?

Simplify the difference quotient $\frac{r(x+h)-r(x)}{h}$ for $r(x)=-3x-2$, where $h\ne 0$.

Find the equation of the line tangent to $v(x)=2x^2-5x$ at $x=-3$.

Simplify the difference quotient $\frac{u(x+h)-u(x)}{h}$ for $u(x)=-x+9$, where $h\ne 0$.

Find the equation of the line normal to $v(x)=-3x^2-2x$ at the point $\left(6,-120\right)$.

Find the equation of the line tangent to $g(x)=-3x^2+5x$ at $x=3$.

Simplify the difference quotient $\frac{g(x+h)-g(x)}{h}$ for $g(x)=-3x-5$, where $h\ne 0$.

Use the definition $r^{\prime }(x)={\lim }_{h\to 0}\frac{r(x+h)-r(x)}{h}$ to find $r^{\prime }(x)$ for $r(x)=6x^2+2x+3$.

Find the equation of the line tangent to $p(x)=-4x^2+4x$ at $x=-6$.

Evaluate ${\lim }_{x\to 4}\frac{x^3-64}{x-4}$ by recognizing it as a derivative.

Simplify the difference quotient $\frac{r(x+h)-r(x)}{h}$ for $r(x)=7x+5$, where $h\ne 0$.