A tangent line to the curve $g$ at the point $(3,-2)$ is given by the equation $y=-3x+7$. What are $g\left(3\right)$ and $g^{\prime }\left(3\right)$?

Find the equation of the tangent line to the curve $h$ at the point $(c,h(c\left)\right)$ where $h\left(x\right)=41x^2$ and $c=1$.

Use the following limit definition to determine the slope of the line tangent to the graph of $f$ at $P$, where $f\left(x\right)=-\frac{4}{x}$ and $P(-4,1)$:

$m_{\text{tan}}=\underset{x\to a}{\lim }\frac{f\left(x\right)-f\left(a\right)}{x-a}$

Graph the tangent line with the equation $y=\frac{13}{9}x+\frac{40}{9}$ and the normal line to the following curve at the given point:

$(x^2+y^2{)}^2=\frac{25}{2}(y^2-x^2)$; $(-1,3)$