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Question 222059: i have a two part symmetry and function related question:
A. Find the point of symmetry of the graph of the cubic function:
f(x)=-x^3+15x^2-48x+45
B. The function has a local minimum at (2,1). At what point does a local maximum occur?
I don't understand how to go about this problem.. help?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A. Find the point of symmetry of the graph of the cubic function:
f(x)=-x^3+15x^2-48x+45
1st derivative -3x^2 + 30x - 48 = 0
2nd derivative -6x + 30 = 0 --> x = 5
f(5) = 55
--> Point of inflection at (5,55)
It appears to be a point of symmetry, but I don't know how to confirm that.
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B. The function has a local minimum at (2,1). At what point does a local maximum occur?
1st derivative -3x^2 + 30x - 48 = 0
--> x = 2 (local minimum)
--> x = 8 (local maximum)
f(8) = 109
local max @ (8,109)
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