How do you find the maximum or minimum of f(x)=3-x^2-6xf(x)=3x26x?

2 Answers
Mar 24, 2018

(-3,12)(3,12)

Explanation:

Since this is a parabolic equation and the value of a<0a<0 it open downwards so it have a absolute maxima. The maximum point is determined by x_(max) = -b/(2a) where b and a are coefficients. This formula is developed using differential calculus.
So,
x_(max) = -b/(2a)
=-(-6)/(2×(-1))
=6/(-2)
:. X_(max) = -3.
Now evaluate f (-3) get the maximum point.

Mar 24, 2018

It's Maximum

Explanation:

The second derivative demonstrates whether a point with zero first derivative is a maximum, minimum or an inflexion point.

f(x) = 3 - x^2 - 6x

f'(x) = (d/(dx)) (3 - 6x - x^2 = -6 - 2x

-6 - 2x = 0 " or" x = -3

f"(x) = (d/(dx)) (-2x - 6 ) = -2

Since f"(x) is negative, it is maximum.

graph{(-x^2 - 6x + 3) [-11.21, 8.79, -13.32, -3.32]}