SOLUTION: f(x)= x^3-3x^2-9x+5 find and classify all stationary points. sketch the graph of fx.

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Question 1032465: f(x)= x^3-3x^2-9x+5
find and classify all stationary points.
sketch the graph of fx.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=+x%5E3-3x%5E2-9x%2B5 ==> f'(x) = 3x%5E2-6x-9+=+3%28x%5E2-2x-3%29.
The stationary points are where f'(x) is zero.
Hence let x%5E2-2x-3+=+%28x-3%29%28x%2B1%29+=+0.
==> x = 3, -1.
Now f"(x) = 6x-6 ==> f"(3) = 12 > 0 ==> local min at x = 3.
f"(-1) = -12 < 0 ==> local max at x = -1.
graph%28+500%2C+500%2C+-15%2C+15%2C+-25%2C+20%2C+x%5E3-3x%5E2-9x%2B5%29