Determine the antiderivative F of “f” , which is defined by f (x) = 4x³ – 6, where F (0) = 3

Given function: f (x) = 4x³ – 6

Now, integrate the function:

∫4x³ – 6 = 4(x⁴/4)-6x + C

∫4x³ – 6 = x⁴ – 6x + C

Thus, the antiderivative of the function, F is x⁴ – 6x + C, where C is a constant

Also, given that, F(0) = 3,

Now, substitute x = 0 in the obtained antiderivative function, we get:

(0)⁴ – 6(0) + C = 3

Therefore, C = 3.

Now, substitute C = 3 in antiderivative function

Hence, the required antiderivative function is x⁴ – 6x + 3
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