SOLUTION: Graph the function -x^3+5x^2-2x+1 A_Find the value of x at which the given f(x) has a local maximum. Round to the nearest hundredth. f' = -3x^2 + 10x - 2 = 0 *[invoke solve_q

Algebra ->  Equations -> SOLUTION: Graph the function -x^3+5x^2-2x+1 A_Find the value of x at which the given f(x) has a local maximum. Round to the nearest hundredth. f' = -3x^2 + 10x - 2 = 0 *[invoke solve_q      Log On


   

Question 1108445: Graph the function -x^3+5x^2-2x+1
A_Find the value of x at which the given f(x) has a local maximum. Round to the nearest hundredth.
f' = -3x^2 + 10x - 2 = 0
*[invoke solve_quadratic_equation -3,10,-2]
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x =
B_Find the value of x at which the given f(x) has a local minimum. Round to the nearest hundredth.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Graph the function -x^3+5x^2-2x+1
A_Find the value of x at which the given f(x) has a local maximum. Round to the nearest hundredth.
B_Find the value of x at which the given f(x) has a local minimum. Round to the nearest hundredth.
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f' = -3x^2 + 10x - 2 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -3x%5E2%2B10x%2B-2+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2810%29%5E2-4%2A-3%2A-2=76.

Discriminant d=76 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+76+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2810%29%2Bsqrt%28+76+%29%29%2F2%5C-3+=+0.213700352153109
x%5B2%5D+=+%28-%2810%29-sqrt%28+76+%29%29%2F2%5C-3+=+3.11963298118022

Quadratic expression -3x%5E2%2B10x%2B-2 can be factored:
-3x%5E2%2B10x%2B-2+=+%28x-0.213700352153109%29%2A%28x-3.11963298118022%29
Again, the answer is: 0.213700352153109, 3.11963298118022. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-3%2Ax%5E2%2B10%2Ax%2B-2+%29

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x = 0.21, 3.12
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f" = -6x + 10
f"(0.21) = positive --> minimum
f"(3.12) = negative --> maximum
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DL the FREE graph software at
www.padowan.dk
Use Ins, enter -x^3+5x^2-2x+1