How do you find the stationary points of a function?

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Answer 1 · 2018-06-26T12:05:31

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As we can see from this image, a stationary point is a point on a curve where the slop is zero

Hence the stationary points are when the derivative is zero

Hence to find the stationary point of $y = f (x)$ $y = f(x)$ , find $\frac{d y}{d x}$ $(dy)/(dx)$ and then set it equal to zero

$\Rightarrow \frac{d y}{d x} = 0$ $=> (dy)/(dx) = 0$

Then solve this equation, to find the values of $x$ $x$ for what the function is stationary

For examples

$y = x^{2} + 3 x + 8$ $y= x^2 + 3x +8$

To find the stationary find $\frac{d y}{d x}$ $(dy)/(dx)$

$\frac{d y}{d x} = 2 x + 3$ $(dy)/(dx) = 2x + 3$

Set it to zero

$2 x + 3 = 0$ $2x+3 = 0$

Solve

$x = - \frac{3}{2} \Rightarrow y = \frac{23}{4}$ $x = -3/2 => y= 23/4$

Hence the stationary point of this function is at $(- \frac{3}{2}, \frac{23}{4})$ $(-3/2 , 23/4 )$