Question

f(x) = 6/(2x+3)for x>=0

Find an expression, in terms of x, for f'(x) and explain how your answer shows that f is a decreasing function.

Answer 1

Any ideas?

Answer 2

f(x) = 6/(2x+3)
f'(x)= -12(2x+3)^2
f'(x) = 0
-12/(2x+3)^2 = 0 then?

Answer 3

@dumbcow @iambatman

Answer 4

Yes, this is ok.
The derivative shows the slope of the curve. If the function is decreasing, its slope will be always negative. You should prove that this derivative will be always negative for \(x \ge 0\).

Answer 5

How?

Answer 6

What can you say about the sign of \(x^2\) ?

Answer 7

y=x^2 lol

Answer 8

\(x^2\) is always positive. So \(-x^2\) is always negative. Now use this to prove that \(f'(x)\) is always negative.

Answer 9

I do not know how to prove.

Answer 10

Ok. If you put any value for \(x\) in \(-\frac{12}{(2x + 3)^2}\) you will get always negative value because of square in the denominator. So this expression wil be always negative.

Answer 11

okay, thanks. :))