SOLUTION: why am I having trouble figuring out concave up and down
determine where the graph of the function is concave up and concave down
f(x)=x^3-6x^2+9x+3
thanks
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-> SOLUTION: why am I having trouble figuring out concave up and down
determine where the graph of the function is concave up and concave down
f(x)=x^3-6x^2+9x+3
thanks
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Question 201627: why am I having trouble figuring out concave up and down
determine where the graph of the function is concave up and concave down
f(x)=x^3-6x^2+9x+3
thanks
You can put this solution on YOUR website! determine where the graph of the function is concave up and concave down
f(x)=x^3-6x^2+9x+3
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I'll assume you are taking a calculus course.
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1st derivative = 3x^2-12x+9
2nd derivative = 6x-12
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The roots of the 1st derivative:
3x^2-12x+9 = 0
x^2-4x+3 = 0
(x-3)(x-1)= 0
x = 1 or x = 3
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Evaluate the 2nd derivative at x = 1 and at x = 3
f''(1) = 6*1-12<0 so f(x) is concave down at x = 1
f''(3) = 6*3-12>0 so f(x) is concave upward at x = 3
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The graph confirms those results:
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Cheers,
Stan H.
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