IB Math Studies Stationary points

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IB Math Studies Stationary points

Postby hill » Mon Apr 15, 2013 7:25 pm

IB Mathematical Studies SL – Calculus, Derivatives, monotonicity, increasing functions, stationary points


How can we find monotonicity (increasing or decreasing) and the turning points for the function .


Thanks
hill
 
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Re: IB Math Studies Stationary points

Postby elizabeth » Mon Apr 15, 2013 7:36 pm

IB Mathematical Studies SL – Calculus, Derivatives, monotonicity, increasing functions, stationary points

The first derivative function is



By setting the derivative equal to zero,

So we know that there is a stationary point when .

From the derivative we know that since when

the function is increasing for

Similarly, since when


the function is decreasing for .

From the above information, we can deduce that the stationary point at is a local maximum.
elizabeth
 
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Re: IB Math Studies Stationary points

Postby hill » Mon Apr 15, 2013 7:44 pm

Thanks Elisabeth!!
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