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