# How do you find the slope of the secant lines of f(x) = 7x^2 at (4, f(4)) and (4+h, f(4+h))?

Jun 5, 2016

$56 + 7 h$

#### Explanation:

Find the points at $x = 4$ and $x = 4 + h$:

$f \left(4\right) = 7 {\left(4\right)}^{2} = 7 \left(16\right) = 112$

$f \left(4 + h\right) = 7 {\left(4 + h\right)}^{2} = 7 \left(16 + 8 h + {h}^{2}\right) = 112 + 56 h + 7 {h}^{2}$

The slope of the secant line is the slope of the line connecting the points $\left(4 , 112\right)$ and $\left(4 + h , 112 + 56 h + 7 {h}^{2}\right)$.

The slope is

$m = \frac{\left(112 + 56 h + 7 {h}^{2}\right) - 112}{\left(4 + h\right) - 4} = \frac{56 h + 7 {h}^{2}}{h} = 56 + 7 h$