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Find the most general antiderivative of the function.

(Check your answers by differentiation.)

$ f(x) = 4x + 7 $

$F(x)=2 x^{2}+7 x+C$

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this problem we're trying to find the most general anti derivative for the human function. So this is um mm F of X equals four X plus seven. And we want to find the anti derivative of this function. So the anti derivative of this function is going to be found. Um Bye first. Mr Yeah, squaring this. So we get X squared over two. So you can give us two X squared. And in class The anti derivative of seven, this constant numbers can be seven x. And then we can't forget to add our constant value in here. Now let's check to make sure we did that correctly when we take the derivative of this. So we take f f. Crime of X. You see that once we change this value right here, the value, regardless of what this value is. Because it's a constant Look at this F prime of X. It's the same exact graph. So what we see is that when we take the derivative, regardless of what psi is, we end up getting the exact same graph for F prime of X. That means that we took the anti derivative properly.

California Baptist University