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Calculate using the definition of the derivative function: `f'(0),f'(-1),f'(9)` if `f:...

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alexa0048 | Student, Grade 11 | (Level 3) eNoter

Posted November 27, 2012 at 4:07 PM via web

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Calculate using the definition of the derivative function:

`f'(0),f'(-1),f'(9)` if `f: RR->RR` and `f(x) = x^4`

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mathsworkmusic | (Level 1) Educator

Posted November 27, 2012 at 7:07 PM (Answer #1)

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We have `f: RR -> RR`  where `f(x) = x^4`

Differentiating we have `f'(x) = 4x^(4-1) = 4x^3`  (multiply by the existing power and reduce the power by one)

Evaluating this function at the points `x=0,-1,9` gives

`f'(0) = 4(0)^3 = 0`,  `f'(-1) = 4(-1)^3 = 4(-1) = -4`

`f'(9) = 4(9)^3 = 4(27) = 108`

f'(0) = 0, f'(-1) = -4, f'(9) = 108

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