Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.) f ''(x) = 24x3 − 15x2 + 8x

Answer 1

Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.)

f ^''(x) = 24x³ − 15x² + 8x

Detailed Solution:

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f^'(x) = ∫f^''(x)dx = ∫(24x³ − 15x² + 8x)dx = 24x⁴/4 − 15x³/3 + 8x²/2 + C = 6x⁴ − 5x³ + 4x² + C

f(x) = ∫f^'(x)dx = ∫(6x⁴ − 5x³ + 4x² + C)dx = 6x⁵/5 − 5x⁴/4 + 4x³/3 + Cx + D

f(x) = (6/5)x⁵ − (5/4)x⁴ + (4/3)x³ + Cx + D

Answer 2

Use Power Rule for integration.