# graph of Sinhx

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

1. 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. 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. Differentiate again.

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

7. 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.