SOLUTION: Find the value of f(2) when f,g are differentiable functions such that (fg)&#8242;(x) = f(x)g&#8242;(x), g(x)<0, for all x, while f(0) = 4

Algebra ->  Functions -> SOLUTION: Find the value of f(2) when f,g are differentiable functions such that (fg)&#8242;(x) = f(x)g&#8242;(x), g(x)<0, for all x, while f(0) = 4      Log On


   

Question 535051: Find the value of f(2) when f,g are differentiable functions such that (fg)′(x) = f(x)g′(x), g(x)<0, for all x, while f(0) = 4
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The product rule says that



If this is equal to f(x)g'(x), then



Since g(x) cannot equal 0, then f'(x) = 0 for all x, then f(x) is a constant function. Since f(0) = 4, then f(2) is also equal to 4.