SOLUTION: Find the derivative using increment steps: (X^2 + 2)(3x -7)

Question 1131247: Find the derivative using increment steps:
(X^2 + 2)(3x -7)
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
f(x)=(x^2+2)(3x-7)
the above foiled out is 3x^3-7x^2+6x-14
3(x+h)^3-7(x+h)^2+6(x+h)-14
3(x^3+3x^2h+3xh^2+h^3)-7x^2-14xh-7h^2+6x+6h-14
3x^3+9x^2h+9xh^2+3h^3-7x^2-14xh-7h^2+6x+6h-14
subtract 3x^3-7x^2+6x-14
f(x+h)-f(x)=9x^2h+9xh^2+3h^3-14xh-7h^2+6h
divide by h
f'(x)=9x^2+9xh+3h^2-14x-7h+6
let h go to 0.
f'(x)=9x^2-14x+6

the derivative is 9x^2-14x+6

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