SOLUTION: What is the maximum y value of V(x)=x(x-10)(x-8)

Question 697551: What is the maximum y value of V(x)=x(x-10)(x-8)
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
What is the maximum y value of V(x)=x(x-10)(x-8)
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V(x) = x^3 - 18x^2 + 80x
V'(x) = 3x^2 - 36x + 80 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=336 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 9.05505046330389, 2.94494953669611. Here's your graph:

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V''(x) = 6x - 36
--> inflection at x = 6
--> local max @ x2, 2.9449...
max = V(x2) =~ 105.0276
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