Question

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))`?

Answer 1

`56+7h`

Explanation:

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

`f(4)=7(4)^2=7(16)=112`

`f(4+h)=7(4+h)^2=7(16+8h+h^2)=112+56h+7h^2`

The slope of the secant line is the slope of the line connecting the points `(4,112)` and `(4+h,112+56h+7h^2)`.

The slope is

`m=((112+56h+7h^2)-112)/((4+h)-4)=(56h+7h^2)/h=56+7h`