I want to evaluate $f''(x)$ for $f(x)=\sin(x)$ and $x=\frac{\pi}{6}$ and then determine the error in the approximation of $f''(\frac{\pi}{6})$.

From previous knowledge, I know that to find an approximation, we need to compute the first derivative to represent the change. Since the question requires the second derivative, I'm a little confused. I appreciate any assistance.

  • $\begingroup$ Are you sure $f''=-f$ perhaps in Taylor series of $\sin$. $\endgroup$ – Nosrati Apr 17 '17 at 12:05
  • $\begingroup$ Yes. that is true $\endgroup$ – Ben Apr 17 '17 at 12:07

HINT: $f^{"}(x)=-\sin x$.
Treat this as $y=f^{"}(x)$

Then simply $$\frac{dy}{dx}=\frac{\Delta y}{\Delta x}$$

Hope it solves your problem?

  • 1
    $\begingroup$ Yes that clears the air thank you $\endgroup$ – Ben Apr 17 '17 at 12:43

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