(Solved): Example 1: Using the graph of \( y=f(x) \) shown below, determine an expression for the slope of t ...

Example 1: Using the graph of \( y=f(x) \) shown below, determine an expression for the slope of the secant line though \( \boldsymbol{P} \) and \( \boldsymbol{Q} \). \[ \begin{aligned} e &=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ &=\frac{f(a+h)-f(a)}{(a+h)-a}=\frac{f(a+h)-f(a)}{h} \end{aligned} \] Using the graph of \( y=f(x) \) shown above, an expression for the slope of the tangent to \( y=f(x) \) at the point \( P(a, f(a)) \) can be determined as follows: