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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

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

Thanks

- hill
**Posts:**0**Joined:**Tue Mar 19, 2013 8:49 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.

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
**Posts:**0**Joined:**Mon Jan 28, 2013 8:09 pm

Thanks Elisabeth!!

- hill
**Posts:**0**Joined:**Tue Mar 19, 2013 8:49 pm

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