How do you find the max or minimum of #f(x)=-7-3x^2+12x#?
Please see the explanation.
Because this question is in precalculus, I am going to assume that you have not, yet, studied differential calculus. Therefore, I am going to show you how to find the minimum or maximum of a quadratic by finding the vertex:
Let's begin by writing the quadratic equation in standard form:
The vertex form of the equation of a quadratic is:
Because "a" in -3, we shall add 0 to the original equation in the form
This allows us to factor a -3 from the first 3 terms:
Set the middle term of the right side of the pattern
Solve for h:
Substitute 2 for every h:
Combine the constant terms:
We can see that the vertex is at
The maximum value that this quadratic achieves is 5, at the x coordinate 2.
First Derivative of
Second deivative of
At the turning point
At the point
Therefore , the maximum value is 5