Question

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

Answer 1

The answer is: `-7`.

The slope of the tangent line to the grapf of `f(x)` in `x=a` is:

`m=f'(a)`.

So:

`y'=-2x+4/(2sqrtx)=-2x+2/sqrtx`, and:

`y'(4)=-2*4+2/sqrt4=-8+1=-7`.