Question

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

Answer 1

Ok for this answer you use a calculator for the times part and for g x you get the times you count too

Answer 2

We want the maximun or minimum of $g(x)=-4x^2+4x-2$

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:

$g'(x)=-8x+4$

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

$0 = -8x+4\\8x=4\\x=\frac{1}{2}$

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.

$g(1/2)=-4(1/2)^2+4(1/2)-2\\g(1/2)=-1+2-2\\g(1/2) = -1$

Therefore, the maximum point $M$ of the function is

$\boxed{M=(0.5,-1)}$

 Glad to help! Wish you great studies.

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