Homework SourseSuppose f3 4 f3 3 and fx 6x 8 Find fx An explanation of
Suppose f(3) = -4, f\'(3) = 3, and f\"(x) = 6x - 8. Find f(x).
An explanation of your answer would help me so much! Thank you.
An explanation of your answer would help me so much! Thank you.
Solution
f\'\'(x) = 6x - 8
f\'(x) = Integral [ f\'\'(x) ] dx
f\'(x) = Integral [ 6x - 8 ] dx
f\'(x) = 3x^2 - 8x + C
f\'(3) = 3
3(3)^2 - 8(3) + C = 3
27 - 24 + C = 3
3 + C = 3
C = 0
f\'(x) = 3x^2 - 8x
f(x) = Integral [ f\'(x) ] dx
f(x) = Integral [ 3x^2 - 8x ] dx
f(x) = x^3 - 4x^2 + C
f(3) = -4
3^3 - 4(3)^2 + C = -4
27 - 36 + C = -4
-9 + C = -4
C = 5
f(x) = x^3 - 4x^2 + 5
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