`f''(x) = 20x^3 - 12x^2 + 6x` Find `f`.

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Chapter 4, 4.9 - Problem 25 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`f''(x)=20x^3-12x^2+6x`

`f'(x)=int(20x^3-12x^2+6x)dx`

Applying the sum rule and power yields,

`f'(x)=20(x^4/4)-12x^3/3+6x^2/2+c_1`

`f'(x)=5x^4-4x^3+3x^2+c_1`

`f(x)=intf'(x)dx`

`f(x)=int(5x^4-4x^3+3x^2+c_1)dx`

`f(x)=5(x^5/5)-4(x^4/4)+3(x^3/3)+c_1x+c_2`

where c_1 and c_2 are constants, simplifying the above

`f(x)=x^5-x^4+x^3+c_1x+c_2`

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