# Math Help - Curve sketching

1. ## Curve sketching

Show that the curve with equation $y = 3\ cosh\ x - x\ sinh\ x$ has a minimum point A on the y-axis. Find the coordinates of A. Show further that the curve has another stationary value between x = 1.9 and x = 3. Sketch the curve.

I’ve done all except curve sketching. How can I sketch this curve? Actually what the process?

2. Originally Posted by geton
Show that the curve with equation $y = 3\ cosh\ x - x\ sinh\ x$ has a minimum point A on the y-axis. Find the coordinates of A. Show further that the curve has another stationary value between x = 1.9 and x = 3. Sketch the curve.

I’ve done all except curve sketching. How can I sketch this curve? Actually what the process?
First try substituting the definitions of cosh x and sinh x in terms of exponentials. Simplify. Consider key features and asymptotic behaviour.

3. Originally Posted by mr fantastic
First try substituting the definitions of cosh x and sinh x in terms of exponentials. Simplify. Consider key features and asymptotic behaviour.
May be I need more information, because I’m so weak on this regard.

By the way, I simplified,

y = 3/2 (e^x + e^-x) – x/2 (e^x - e^-x)
= e^2x (3/2 – x/2) + 1/2 (3/2 + x/2)

What to do next? As I get a minimum point A is (0, 3). And another stationary point lies between 1.9 and 2. Have to working on this to find 2nd stationary point?

Do you have any suggestions/notes/useful websites to learn this kind of stuff, will help me lot to understand.