IB Maths SL Second Derivative test

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IB Maths SL Second Derivative test

Postby Oliver » Thu Mar 21, 2013 3:44 pm

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
Oliver
 
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Re: IB Maths SL Second Derivative test

Postby miranda » Thu Mar 21, 2013 3:47 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!! :) :)
miranda
 
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Re: IB Maths SL Second Derivative test

Postby Oliver » Thu Mar 21, 2013 3:48 pm

thank you miranda!
Oliver
 
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