0
$\begingroup$

I've been trying to learn derivatives recently. I have troubles with finding local minimums and maximums given an equation

I have understood this far

$y=2x^3-9x^2+12x-5$

$dy/dx= 6x^2-18x+12$

$x=1$ or $x=2$

$f(1)=0$
Point A $(1,0)$

$f(2)=-1$
Point A $(2,-1)$

What I do not understand is how one categorizes the points, either as minimums or maximums. I have looked around but I can't make sense of the explanations.

$\endgroup$
1
$\begingroup$

If:

  • ${d^2 y \over d x^2} > 0:$ local minimum
  • ${d^2 y \over d x^2} < 0:$ local maximum
  • ${d^2 y \over d x^2} = 0:$ point of inflection

If the second derivative is positive, that means the first derivative (i.e., the slope) keeps getting larger at the point in question. The only way for that to be is for the point to be a local minimum.

Conversely if the second derivative is negative.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.