find equation of tangent line

[tonytouch311]

f is a differentiable function with f(2)=3 and f'(2)=5. g is defined by g(x)=x*f(x). find the line tangent to the graph of g at poin2 where x=2.



-i understand that the slope is 5. and on the curve are points (2,3). im just confused about the g(x). 2*3 is 6, but is that put there to confuse me?

 

[tkhunny]

It is "the g(x)" part that is interesting! You must understand the product rule for differentiation.

You have g(2) = 2*f(2) = 2*3 = 6, giving a point (2,6)

What else do you need to determine a unique line through this point?

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

Whoops! I hadn't intended to do all the work, but there it is. I guess I'll leave it.

 

[tonytouch311]

Thank you. I believe I understand it now, i believe the equation for the tangent line would be y=-7x+20

 

[tkhunny]

What did you get for g'(x) evaluated at x = 2?