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.