Question

let f(x) = 5x [(5-5x)^(1/2)],
find the equation of the line tangent to the graph of f at x=-2.

Answer 1

Do you mean \[y=f(x)=5x \sqrt{5-5x}\]?
If so, differentiate to find the slope at x=-2

\[dy/dx=1/2\times5x(5-5x)^(-1/2)\times-5 = -25/2\times(5-5x)^(-1/2)\]

Answer 2

but I need it in the form y=mx+b