Answer:
The function has a maximum
The maximum value of the function is
[tex]f (-1) = 11[/tex]
Step-by-step explanation:
For a quadratic function of the form:
[tex]ax ^ 2 + bx + c[/tex] where a, b and c are the coefficients of the function, then:
If [tex]a <0[/tex] the function has a maximum
If [tex]a> 0[/tex] the function has a minimum value
The minimum or maximum value will always be at the point:
[tex]x=-\frac{b}{2a}\\\y=f(-\frac{b}{2a})[/tex]
In this case the function is: [tex]f(x) = -5x^2 - 10x + 6[/tex]
Note that
[tex]a = -5,\ a <0[/tex]
The function has a maximum
The maximum is at the point:
[tex]x=-\frac{-10}{2(-5)}[/tex]
[tex]x=-1[/tex]
[tex]y=f(-1)[/tex]
[tex]y= -5(-1)^2 - 10(-1) + 6[/tex]
[tex]y= 11[/tex]
The maximum value of the function is
[tex]f (-1) = 11[/tex]
