Question

The tangent line to the graph of a function g at the point x = 6 is y = 16-3x. Find the tangent line to the graph of y = x g(x) at x = 6. Put your answer into slope-intercept form.

Answer 1

y = x g(x)

y ' = x' g(x) + x*g ' (x) ... derive both sides with respect to x

y ' = 1* g(x) + x*g ' (x)

y ' = g(x) + x*g ' (x)

Now plug in x = 6

y ' = g(6) + x*g ' (6)

do you see how to finish up?