Thread: First derivative in relation to the second.

1. First derivative in relation to the second.

I have a problem with a question that is on one of my assignments. I know I can't put the actual question up due to regulation on this forum and my teacher's personal rules, however, i was wondering, in general terms, if the first derivate at a point, say maybe f'(3)=0, would that automatically mean that the second derivative at that point is 0 too?

2. Re: First derivative in relation to the second.

No. Suppose f'(x)=x^2 -9 Then f'(3)=0 Now f''(x)=2x so f''(3)=6

3. Re: First derivative in relation to the second.

Then how would I figure, based on a chart given x and the f(x) values, the derivative of the function at that point?

4. Re: First derivative in relation to the second.

Originally Posted by ltlbit94
Then how would I figure, based on a chart given x and the f(x) values, the derivative of the function at that point?
You would either need to get a least-squares function for your curve, if you don't already know the rule for the function, which you can then differentiate, or you can simply work out the gradient of the chords between successive data points. Neither way is exact though.