# graph of Sinhx

Discussion in 'Mathematics' started by fudgesweets, Jan 31, 2011.

1. ### fudgesweetsNew commenter

hi all,

I am a bit confused. The graph of y=Sinhx seems to have a point of inflection about x=0. However if I differentiate this function then y'=Coshx and Coshx does not ever equal zero, bringing me to the conclusion that there are no turning points on that graph??

The website http://nrich.maths.org/2377&part=solution describes the point at the origin as a point of inflection also??

2. ### fudgesweetsNew commenter

hi all,

I am a bit confused. The graph of y=Sinhx seems to have a point of inflection about x=0. However if I differentiate this function then y'=Coshx and Coshx does not ever equal zero, bringing me to the conclusion that there are no turning points on that graph??

The website http://nrich.maths.org/2377&part=solution describes the point at the origin as a point of inflection also??

3. ### Polecat

Differentiate again.

4. ### briceanusNew commenter

Following from Polecat, a point of inflexion/inflection does not have to be at a point where the gradient of the curve is zero. It's just that in A-level maths, we only tend to look at f'(x)=0 AND f''(x) = 0 when analysing inflections.

5. ### coyoteNew commenter

You solve y'=0 to find maxima or minima. The point of inflection at x=0 for sinhx is neither.
At this point, the gradient changes from decreasing to increasing.

6. ### DMNew commenter

You are looking at the wrong graph. The catenary is the interesting one!

7. ### David GetlingLead commenter

Can't remember if it's in the A-Level syllabus, but I would mention it anyway. At a point of inflection a region of a graph changes from concave to convex, or vice versa. A nice little fact, worth mentioning to students.