Sketch, showing any stationary points and inflexions. y=xInx

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should remember that you may find the stationary points solving the equation `f'(x) = 0`  such that:

`f'(x) = (x*ln x)' `

You should use the product rule such that:

`f'(x) = x'*ln x + x*(ln x)'`

`f'(x) = ln x + x/x`

`f'(x) = ln x + 1`

You need to solve the equation `f'(x) = 0`  such that:

`ln x + 1 = 0 =gt ln x = -1 =gt x = e^(-1) =gt x = 1/e`

Hence, the function has a stationary point at `x = 1/e.`

You should solve the equation `f''(x) = 0`  to find the inflection points, if any:

`f''(x) = (ln x + 1)'`

`f''(x) = 1/x`

`1/x ! = 0`

Hence, the function has no inflection points.

Thus, the function has a stationary point at `x = 1/e`  and it has no inflection points.

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