calculus prob.?

Question

let f be a differentiable function with f(2) = 3 and f '(2) = -5, and let g be the function defined by g(x) = xf(x). Which of the following is an equation of the line tangent to the graph of g at the point where x = 2:
a)y=3x
b)y-3=-5(x-2)
c)y-6=-5(x-2)
d)y-6=-7(x-2)
e)y-6=-10(x-2)

Answer 1

Ah ha, now we see the real question.

This is an application of the product rule.

g(x) = xf(x)
g'(x) = xf'(x) + (1)f(x) [by the product rule]
g'(2) = 2f'(2) + f(2) = 2(-5) + 3 = -7

Also,

g(2) = 2f(2) = 2(3) = 6

So the point is (2, 6), and the slope is -7....

y - 6 = -7(x - 2)

Answer 2

You should go ask your teacher rather than have strangers do your homework.