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

Question

f'''(t) = sqrt (t) - 6cos(t)

Answer 1

Assuming this is not a test....... and that this is the third derivative since it is so small

f'''(t) = sqrt(t)-6cos(t)

f''(t) = (2/3) t^(3/2) -6 sin (t) +C

f' (t) = (2/3) (2/5) t^(5/2) +6 cos(t) +Ct +D

f(t) = (2/3)(2/5) (2/7) t^(7/2) +6 sin (t) +(1/2)Ct^2 +Dt +E

You will need to multiply the fraction coefficients to simplify