## Precalculus (6th Edition) Blitzer

The slope of the tangent line to the graph of a function $y=f\left( x \right)$ at $\left( a,f\left( a \right) \right)$ is given by $\underset{h\to 0}{\mathop{\lim }}\,$ $\frac{f\left( a+h \right)-f\left( a \right)}{h}$ provided that this limit exists. Also, the derivative of the function is given by ${f}'\left( x \right)=\underset{h\to 0}{\mathop{\lim }}\,\frac{f\left( a+h \right)-f\left( a \right)}{h}$. Thus, the derivative of a function $f$ gives the slope of $f$ for any value of x in the domain of $f'$.