G(x) = -4x2 + 4x – 2
What is the maximum or minimum step by step

We want the maximun or minimum of

Firstly, notice that we have a leading coefficient of -4, wich means our parabola is concave down. Thus, our function will have a maximum.

To find what is the maximum, let's firstly find on wich value of x it happens. We'll start by taking the first derivative of the function:

To find the extremes of the function, we just need to find where the derivative equals zero. Setting g'(x)=0 we have

So we found that the x coordinate of the maximum is x=1/2. To find the y coordinate we just need to substitute the value of x into the original function.

Therefore, the maximum point of the function is

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step-by-step explanation: