## IB Math Studies Stationary points

Number and algebra, Descriptive statistics, Logic, sets and probability, Statistical applications, Geometry and trigonometry, Mathematical models, Introduction to differential calculus.

### IB Math Studies Stationary points

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 $y=-x^2+7$.

Thanks
hill

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Joined: Tue Mar 19, 2013 8:49 pm

### Re: IB Math Studies Stationary points

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

The first derivative function is

$f'(x)=-2x$

By setting the derivative equal to zero, $f'(x)=-2x=0\Rightarrow x=0$

So we know that there is a stationary point when $x=0$.

From the derivative we know that since $f'(x)=-2x>0$ when $x<0$

the function is increasing for $x<0$

Similarly, since $f'(x)=-2x<0$ when $x>0$

the function is decreasing for $x>0$.

From the above information, we can deduce that the stationary point at $x=0$ is a local maximum.
elizabeth

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Joined: Mon Jan 28, 2013 8:09 pm

### Re: IB Math Studies Stationary points

Thanks Elisabeth!!
hill

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Joined: Tue Mar 19, 2013 8:49 pm