Find the Antiderivative for f(x)=0 with F(0)=3: A Solution Guide

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In summary, the antiderivative of f(x)=0 is any constant value, and F(0)=3 is used to find a specific solution for the antiderivative. Solving for the antiderivative is a simple process, and it can be represented as a function. It is possible for the antiderivative to have multiple solutions that satisfy the condition of F(0)=3.
  • #1
tandoorichicken
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The problem:
For function f(x), find an antiderivative F(x) taking the value indicated:
f(x)=0; F(0)=3

ummm... how?
 
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  • #2
let y=F(x)
f(x)=dy/dx=0
[inte](dy/dx)dx=[inte]0dx
y=C=F(x)
If F(0)=3, then C=3.
 
  • #3


The antiderivative of a constant function is simply the original function multiplied by x. In this case, since f(x)=0, the antiderivative F(x) would be 0 multiplied by x, which is still 0. Therefore, the antiderivative for f(x)=0 with F(0)=3 would be F(x)=3. This is because when we take the derivative of F(x), which is 3, we get back to the original function f(x)=0.
 

FAQ: Find the Antiderivative for f(x)=0 with F(0)=3: A Solution Guide

What is the antiderivative of f(x)=0?

The antiderivative of f(x)=0 is any constant value, since the derivative of a constant is always 0. Therefore, the antiderivative for f(x)=0 with F(0)=3 can be any constant value, such as 3, 5, or -2.

How do you solve for the antiderivative of f(x)=0?

Solving for the antiderivative of f(x)=0 is a simple process. Since the derivative of a constant is always 0, the antiderivative can be any constant value. In this case, since F(0)=3, the antiderivative is simply 3.

Can the antiderivative for f(x)=0 be a function?

Yes, the antiderivative for f(x)=0 can be a function. Since the antiderivative can be any constant value, it can also be represented as a function, such as F(x)=3 or F(x)=5.

What is the significance of F(0)=3 in finding the antiderivative for f(x)=0?

F(0)=3 is used to find the specific value of the constant in the antiderivative. Since the antiderivative can be any constant value, F(0)=3 narrows down the possibilities and allows us to find a specific solution for the antiderivative.

Is it possible for the antiderivative of f(x)=0 to have multiple solutions?

Yes, it is possible for the antiderivative of f(x)=0 to have multiple solutions. Since the antiderivative can be any constant value, there can be multiple solutions that satisfy the condition of F(0)=3. For example, F(x)=3, F(x)=5, and F(x)=-2 are all valid solutions for the antiderivative of f(x)=0 with F(0)=3.

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