antiderivative of Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f (x) = 6 x 5 - 8x4 - 9x2.) f (x) = 6x5 - 8x4 - 9x2 the function.

x^6 - (8/5) x^5 - 3x^3 + C.

Step-by-step explanation:

f (x) = 6x^5 - 8x^4 - 9x^2.

Using the general form antiderivative of Ax^m = Ax (m+1) / (m+1) + C:

Antiderivative = 6 * x^ (5+1) / 6 - 8 * x^ (4+1) / 5 - 9 * x^ (2+1) / 3 + C

= 6x^6/6 - 8x^5/5 - 9x^3/3 + C

= x^6 - (8/5) x^5 - 3x^3 + C.

Differentiating:

f' (x) = 6x^ (6-1) - 8 x^ (5-4) - 9x^ (3-1) + 0

f' (x) = 6x^5 - 8x^4 - 9x^2.