# Math Help - Hyperbolic maximum turning point

1. ## Hyperbolic maximum turning point

Hi, need a bit of help with this question.

The curve $y = -x + \tanh{48x}$, $x \ge 0$ has a maximum turning point at A, find the x co-ordinates of A in exact logarithmic form.

Differentiated the equation to get $x = \frac{ln{(7 \pm 4\sqrt{3})}}{49}$, which turns out to be right.

In the answers though, they only have $x = \frac{ln{(7 + 4\sqrt{3})}}{49}$, at first I though this was because you cannot take a natural log of a minus number, but $7 - 4\sqrt{3}$ is a positive number.

Any ideas?

2. I could differentiate it again and then see whether it is a positive or negative number, to determine whether it is a maximum or minimum, but was just wondering if there was an easier method than this.

Also, they have not made any reference to this in the answers :S

3. ## Turning points

Hi Craig -

I haven't done the differentiation, but presumably the other root gives a minimum?