Question

Determine whether the given function has a maximum or a minimum value. Then, find the maximum or minimum value of the function. f(x) = -2x^2 + 10x + 6

a. The function has a minimum value. The minimum value of the function is –31.5.

b. The function has a maximum value. The maximum value of the function is 18.5.

c. The function has a maximum value. The maximum value of the function is –31.5.

d. The function has a minimum value. The minimum value of the function is 18.5.

Answer 1

Answer:

It has a maximum at x=2.5

Step-by-step explanation:

It's a parabola so finding the x value is easy

https://simplisico.com/share/q/z2gWMnIzbRlLn6ucL8NQmhmC

If you want to find that y value you just need to plug 2.5 into the original function

Answer 2

Answer:

b. The function has a maximum value. The maximum value of the function is 18.5.

Step-by-step explanation:

Let's consider the equation of a parabola.

f(x) = -2x² + 10x + 6

where,

a: -2

b: 10

c: +6

The sign of "a" determines the openness of the parabola. Since a < 0, the parabola is open downwards and has a maximum.

We can find "x" of the vertex using the following expression.

x(v) = -b/2a = -10/2.(-2) = -2.5

We can find the "y" of the vertex by replacing this x in the equation

y(v) = -2.(2.5)² + 10.(2.5) + 6 = 18.5

The vertex (maximum) is (2.5, 18.5).