# calculus

posted by .

f(x) = 6x^2 -8x +3

how would I find the most general antiderivative of the function. I also have to check my answer by differentiation.

Would I have to find the derivative first? (I got 12x -8)
What are the steps to solving a problem like this?

No, don't do the derivative first. Do that on the integral, to check your answer.

I use the word "integral" for what you are calling "antiderivative". You can say I am old-fashioned, but I don't see a need for a longer word.

The general rule for integrating any
a x^n term
is that the integral is
a x^(n+1)/(n+1)
When you have a polynomial, as you do here, the integral is the sum of the integrals of the terms.

The first term of the integral is
6 x^3/3 = 2 x^3. Take the derivative of that and you get the original 6 x^2 back, so it is the right answer.

Now you do the other terms, and add them up.

Remember that the most general integral has an arbitrary constant term added.

## Similar Questions

1. ### Math - Calculus Question.

hey can someone explain to me the relationship between the chain rule and implicit differentiation?
2. ### derivative am i right or wrong

what is the antiderivative of 1/(x^2-2x+2)?
3. ### increasing decreasing calc

f(x)=x^3=12x-24 f'(x)=3x^2+12=0 3x^2=-12 x^2=-4 what is x. would it be x=-2 and 2 because i have to find the interval where the function is increasing or decreasing. i already know how to find the answer but i just got confused on …
4. ### Calculus (Help)

Also I would like to know how to set this problem up in finding the answer: Find the second derivative. y= sqrt(3x+4) Thanks, P.S. I tried taking 3x+4 and squaring it to the 1/2. I thought that might've been the same, then I took the …
5. ### Calculus

Use a symbolic differentiation utility to find the derivative of the function g(x)=xã((x^2)+1). Use the utility to graph the function and is derivative on the same set of coordinate axes. Describe the behavior of the function that …

Find d^2y/dx^2 by implicit differentiation. x^(1/3) + y^(1/3) = 4 I know that first you must find the 1st derivative & for y prime I got 1/3x^(-2/3) + 1/3y^(-2/3) dy/dx = 0 Then for dy/dx I got dy/dx = [-1/3x^(-2/3)] / [1/3y^(-2/3)] …
7. ### Math

Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative. Remember to use ln |u| where appropriate.) (x^5+x^3+8x)/x^4
8. ### Calculus Help and Check

1)Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative. Remember to use ln |u| where appropriate.) f(x) = (1/5)−(3/x) -----> (x/5)-3lnx+C …
9. ### CALC 1

Suppose that h is a function with h'(x) = xe^x. Find all intervals where the function h is concave up. Now, I understand that concavity is determined by the second derivative, so what my question here is, is it just taking the first …
10. ### Please check my Calculus

1. Find all points of inflection of the function f(x)=x^4-6x^3 A. (0, 0) B. (0, 0), (9/2, -2187/16) C. (3, -81) D. (0, 0), 3, -81) E. none of these I got D. I found the second derivative and solved for x and plugged values into original …

More Similar Questions