Find C(x) if C'(x) = 5x2 - 7x +4 and C(6) = 260.
SOLUTION :
C’ (x) = 5x^2 - 7x + 4
=> C (x) = ∫ (5x^2 - 7x + 4) dx
=> C (x) = 5/3 x^3 - 7/2 x^2 + 4x + A (A is a constant)
=> C(6) = 5 (6)^3 / 3 - 7(6)^2 / 2 + 4(6) + A
=> 260 = 360 - 126 + 24 + A
=> 260 = 258 + A
=> A = 260 - 258 = 2
So, C(x) = 5/3 x^3 - 7/2 x^2 + 4x + 2 : 2nd Option (ANSWER)
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