# How do you find the slope of the tangent line to the graph of f(x)=-x^2+4sqrt(x) at x = 4?

Mar 25, 2015

The answer is: $- 7$.

The slope of the tangent line to the grapf of $f \left(x\right)$ in $x = a$ is:

$m = f ' \left(a\right)$.

So:

$y ' = - 2 x + \frac{4}{2 \sqrt{x}} = - 2 x + \frac{2}{\sqrt{x}}$, and:

$y ' \left(4\right) = - 2 \cdot 4 + \frac{2}{\sqrt{4}} = - 8 + 1 = - 7$.