SOLUTION: 6) Given the curve y = x^3 - 3x^2 - 9x+11, find dy/dx.Hence obtain a) the x-coordinates of the points where the gradient is 15, b) the coordinates of the points where the gradien

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Question 1190557: 6) Given the curve y = x^3 - 3x^2 - 9x+11, find dy/dx.Hence obtain
a) the x-coordinates of the points where the gradient is 15,
b) the coordinates of the points where the gradient is zero.
Found 2 solutions by Alan3354, math_helper:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
Given the curve y = x^3 - 3x^2 - 9x+11, find dy/dx.
dy/dx = 3x^2 - 6x - 9
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Hence obtain
a) the x-coordinates of the points where the gradient is 15
f'(x) = 3x^2 - 6x - 9 = 15
3x^2 - 6x - 24 = 0
x^2 - 2x - 8 = 0
(x+2)*(x-4) = 0
x = -2
x = 4
Find the ordinates for each x.
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b) the coordinates of the points where the gradient is zero.
3x^2 - 6x - 9 = 0
Solve for x and y.

Answer by math_helper(2461) (Show Source):
You can put this solution on YOUR website!

dy/dx = (making use of d()/dx = )
a)
= 15
= 0
factor:
= 0
x = 4 and x = -2 are solutions

Check:
x=4 ==> (ok)
x=-2 ==> (ok)
b)
= 0
factor:
= 0
x=-1 and x=3
be sure to check these (plug each value of x into )