Question

Find the equation of the tangent line to the graph of f(x)=2xln(x+7) at x=−5.

Answer 1

well, we know x = -5
and y = f(x)

and so, the equation of the tangent line will be \(\bf y-f(x_0)=m(x-x_0)\implies y-f(x_0)={\color{brown}{ \frac{dy}{dx}}}(x-x_0)\)

Answer 2

so, "x" is given, you can get "y" from f(x)
all you need really is the slope, or derivative, at x = -5
and plug it in the point-slope form :)

Answer 3

keep in mind that \(\bf f(x)=2xln(x+7)\implies f(x)=ln\left[ (x+7)^{{\color{brown}{ 2x}}} \right]
\)

Answer 4

okay