Question 65967: Please help me sketch this equation: X^3-X^2-16X+16
I need to find the X and Y intercepts and the max and min points.
I figured out the y-intercept to be (0,16) and the x-intercepts to be (1,0), (4,0) and (-4,0).
I am having trouble with the max/min points. This is what I have so far.
I took the derivitive for the max.
Y=X^3-X^2-16X+16
Y=3X^2-2X-16
let y=0
0=(3x-8)(x+2)
x=8/3 x=-2
This is where I get stuck. If you could help me the max/min, that would be great. Thankyou!
Sincerely,
Leanne Spence
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! What you've done so far looks good!
Now that you have the x-coordinates of the maximum and minimum points of the curve, substitute these into the original cubic equation and solve for y.
You shoul get:
y = 36 and y = -14.8148...
You can see by inspection that the maximum is at (-2, 36) and the minimum is at (2.67, -14.815)
Here's what the graph looks like:
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