Posted by nic on Tuesday, January 25, 2011 at 10:30pm.
Let f(x)=5x³-6x, then
f(-1)=5(-1)³-6(-1)=1
Slope at (x, f(x)) is given by dy/dx=f'(x)
f'(x) = dy/dx = 15x³-6
f'(-1)= 15(-1)²-6=9
Therefore you need a line with a slope of 9 to pass through the point (-1,1).
The standard equation for this is:
(y-y1)=m(x-x1)
where m=9, y1=-1, x1=1
(y-(-1)) = 9(x-1)
y=9x-9-1
y=9x-10 (slope of 9 and passes through (-1,1))
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