The function is .

Find the first derivative with respect to x.

At turning points or does not exist.

Compare the equation with the general form of quadratic equation .

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Substitute in the quadratic formula : .

If x = 2.6 then

If x = 1.4 then .

The turning points are .

At points of inflection or does not exist.

Find the second derivative with respect to x.

If x = 2 then .

The point of inflection is .

The function is .

Differentiate with respect to x.

Apply quotient rule:

The function is .

Differentiate with respect to x.

The function is .

Differentiate with respect to x.

Again differentiate with respect to x.

To find the critical numbers, or does not exist.

The function does not exist when .

The imaginary numbers are negligible, so the critical number is x = 0.

Apply second derivative test:

The relative maximum point (0, 1).

To find the points of inflection, or does not exist.

The function does not exist when 

The imaginary numbers are negligible.

The points of inflections are (1, 1/2) and (-1, 1/2).

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