## Trending News

Promoted

Anonymous

# What should be the graph of the the function with these given properties?

f(5) = 12, f '(x) <0 for x < 0 and x > 5, f '(x) >0 for 0 <x < 5, f '(5) = 0, f(0) and f '(0) do not exist

### 1 Answer

Relevance

- s kLv 79 years agoFavorite Answer
f'(5) = 0, f'(0) DNE => f'(x) = a(x - 5)/x

f'(1) = -4a > 0, let a = -1.

f'(x) = (5 - x)/x

f'(-1) = (5 + 1)/(-1) = -6 < 0

So we're good.

Then f(x) = ∫f'(x)dx

= ∫(5/x - 1)dx = 5ln|x| - x + C.

f(5) = 12 = 5ln(5) - 5 + C

17 - 5ln(5) = C

So f(x) = 5ln|x| - x + 17 - 5ln(5).

Still have questions? Get your answers by asking now.