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

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If f (x) = 12x^3 - 2x^2 - 17 and f(1) = 8 , find - id1232217187135914, pgfrkypory2107

Ответ:

hopeR13

30.01.2022

Mathematics

f(x) = 3x⁴ - $\frac{2X^{3} }{3}$ - 17x + $\frac{68}{3}$

Step-by-step 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 - $\frac{2X^{3} }{3}$ - 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 - $\frac{2(1)^{3} }{3}$ - 17(1) + C

8 = 3 - $\frac{2}{3}$ - 17 + C

C =8 - 3 + 17 + $\frac{2}{3}$

C = 22 + $\frac{2}{3}$

C = $\frac{66 + 2}{3}$

C = $\frac{68}{3}$

f(x) = 3x⁴ - $\frac{2X^{3} }{3}$ - 17x + $\frac{68}{3}$

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

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