A curve has equation the follwing equation.
y = 3x^3− 6x^2+4x+2.
Show that the gradient of the curve is never negative
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`y = 3x^3-6x^2+4x+2`
The gradient of a curve is given by the its first derivative as follows.
`y' = 9x^2-12x+14`
`=9[(x-12/18)^2 + 4/9 – (12/18)^2]` By completing square
We know that `(x-2/3)^2 >= 0` always for every x.
There for y' or gradient will be greater than or equal to 0.That means gradient never become negative.
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