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

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Answer 1 · 2016-06-05T20:02:03

$56+7h$

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

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

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