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

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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]
=================
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)   (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.
=================
f' = -3x^2 + 10x - 2 = 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=76 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.213700352153109, 3.11963298118022. Here's your graph:

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

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