what is the antiderivative?

Question

what would be the antiderivative of f(x)=12x³-9x²+8x-3

 

I believe it would be 3x⁴-3x³+4x²-3x+7 , is that correct?

Answer 1

Lets check to see if your anti-derivative is correct.  To do this, we derive your answer, and we should get back the original problem.

 

d/dx(3x⁴ - 3x³ + 4x² - 3x + 7) =

 

12x³ - 9x² + 8x - 3

 

 

Your anti-derivative is good, but just replace the 7 with C , since C is any arbitrary constant.

 

 

Answer 2

Hi Jazzie

It is almost correct, however the constant number(7) you put is not know unless we know the initial value of its antiderivative F(0). (F(x)=f'(x)) If F(0)=7 then your answer is correct. Otherwise you should add a constant parameter such as b.

 

Hope this helps,

Ehsan