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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the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

the answer is c

step-by-step explanation: i took a test with this question on it