Question

*medal to most helpful* "Find the values of a and b so that the function f(x)=axe^(-bx) has a local maximum at the point (2,10)." Ahhh, so confusing. Anyone wanna start me off, please?

Answer 1

Here are some hints to start you off.
Given \(f(x)=a.x. e^(-bx)\)
1. Since (2,10) is a point on the curve, we can use f(2)=10 to get a relation between a and b.
2. If (2,10) is a local maximum, it means that f'(2)=0. So calculate the derivative f'(x) and equate it to zero at x=2. This gives another equation between a and b.
Use relations obtained in 1 and 2 to solve for a and b.
3. double check that f"(x) (second derivative) is negative at x=2, or f"(2)<0 for f(2) to be a maximum.

Answer 2

Thanks, I solved this and forgot to close the question. I'll give you the medal anyway. :) Sorry for the trouble!