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If f'(x) = 12x^3 - 2x^2 - 17 and f(1) = 8 , find f(x).

1 Answer

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Answer:

f(x) = 3x⁴ -
(2X^(3) )/(3) - 17x +
(68)/(3)

Explanation:

To find f'(x), we will follow the steps below:

We will start by integrating both-side of the equation

∫f'(x) = ∫(12x^3 - 2x^2 - 17)dx

f(x) = 3x⁴ -
(2X^(3) )/(3) - 17x + C

Then we go ahead and find C

f(1) = 8

so we will replace x by 1 in the above equation and solve for c

f(1) = 3(1)⁴ -
(2(1)^(3) )/(3) - 17(1) + C

8 = 3 -
(2)/(3) - 17 + C

C =8 - 3 + 17 +
(2)/(3)

C = 22 +
(2)/(3)

C =
(66 + 2)/(3)

C =
(68)/(3)

f(x) = 3x⁴ -
(2X^(3) )/(3) - 17x +
(68)/(3)

User Santosh Dangare
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7.8k points

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