If f’’(x) =x-2, f’(2) =-5, and f(0)=-4 then what is f(6)?

Question

If f’’(x) =x-2, f’(2) =-5, and f(0)=-4 then what is f(6)?

Answer 1

f'(x) = ∫f"(x)dx = (1/2)x² - 2x + C₁

Since f'(2) = -5, we have -2 + C₁ = -5. So, C₁ = -3

f'(x) = (1/2)x² - 2x - 3

f(x) = ∫f'(x) dx = (1/6)x³ - x² - 3x + C₂

Since f(0) = -4, C₂ = -4

So, f(x) = (1/6)x³ - x² - 3x - 4.

Therefore, f(6) = 36 - 36 - 18 - 4 = -22

Answer 2

Hello,

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Thank You,

Michael H.

Answer 3

Hi Katrina!

Hope you're doing well!

I've answered in your question in the video attached. Sorry for any lagging or stuttering as my WiFi's a little spotty.

Feel free to let me know if you have any questions.

Best,

Daniel I.