# How do you find the slope of the tangent line to the graph of the function g(x) = 4 − 8x^2 at the point (7, -388)? can somebody explain what i need to do please? and my math book isnt explaining it well by the way.?

Jun 5, 2015

When you need the slope of the tangent you first evaluate the derivative and then you evaluate it at the point you want, the number you get will be your slope.

For example, in your case you have:

$g \left(x\right) = 4 - 8 {x}^{2}$

The derivative is:

$g ' \left(x\right) = - 16 x$

If you use $x = 7$ (the coordinate $x$ of your point) in it you get:
$g ' \left(7\right) = - 16 \cdot 7 = - 112$ which is the slope you need.