Question 1190557
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.