Let f′′′(t)=-1t+9√t. Find the most general formula

Question

Let f′′′(t)=-1t+9√t

Find the most general formula for f′′(t). If an arbitrary constant must be used here, use an upper-case "C".

(b) Based on your answer to (a), find the most general formula for f′(t). If another new arbitrary constant must be used here, use an upper-case "D". (

c) Based on your answer to (b), find the most general formula for f(t). If another new arbitrary constant must be used here, use an upper-case "E".

Answer 1

f''(t) = ∫f'''(t)dt = -(1/2)t² + 6t^3/2 + C

f'(t) = ∫f"(t)dt = -(1/6)t³ + (12/5)t^5/2 + Ct + D

f(t) = ∫f'(t)dt = -(1/24)t⁴ + (24/35)t^7/2 + (C/2)t² + Dt + E