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IB Mathematics SL – Derivatives, Turning points, 2nd derivative test

How can we find coordinates and nature of all the stationary points of the function ?

Thanks

How can we find coordinates and nature of all the stationary points of the function ?

Thanks

- Oliver
**Posts:**0**Joined:**Mon Jan 28, 2013 8:08 pm

IB Mathematics SL – Derivatives, monotonicity, increasing functions, turning points

We know that

If and then at the function has a minimum turning point

If and then at the function has a maximum turning point

If and and the second derivative function changes sign around then at the function has a stationary point of inflection.

The first derivative function is

By setting the derivative equal to zero,

So we know that there are stationary points when .

By substituting into the original equation

and

Thus the coordinates of the stationary points are

The second derivative function is

By substituting the values of the stationary points into second derivative function

, so is a local minimum point

and

, so is a local maximum point

Hope these help!!

We know that

If and then at the function has a minimum turning point

If and then at the function has a maximum turning point

If and and the second derivative function changes sign around then at the function has a stationary point of inflection.

The first derivative function is

By setting the derivative equal to zero,

So we know that there are stationary points when .

By substituting into the original equation

and

Thus the coordinates of the stationary points are

The second derivative function is

By substituting the values of the stationary points into second derivative function

, so is a local minimum point

and

, so is a local maximum point

Hope these help!!

- miranda
**Posts:**268**Joined:**Mon Jan 28, 2013 8:03 pm

thank you miranda!

- Oliver
**Posts:**0**Joined:**Mon Jan 28, 2013 8:08 pm

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