Question

Suppose F is an antiderivative of f and A is an area function of f. What is the relationship between f and A? What is the relationship between F and A?

Answer 1

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the  relationship between F and A is  x 
A(x) = ∫ f(x)dx = F(x) -F(0) 
0

Answer 2

The relationship between f and A is $\boxed{A\left( x \right) = \int {f\left( x \right)dx} }$ and the relationship between F and A is $\boxed{F\left( x \right) = A\left( x \right) + C}.$

Further explanation:

Given:

F is an anti-derivative of fand A is an area function of f.

Explanation:

The relationship between f and A can be obtained as follows,

$A\left( x \right) = \int {f\left( x \right)dx}$

If F is an anti-anti-derivative of the function f and A is the area function of f, then the relationship between A and F can be obtained as follows,

$F\left( x \right) = A\left( x \right) + C$

Here, $A\left( x \right)$ the area in terms of x and C is the constant.

The relationship between f and A is $\boxed{A\left( x \right) = \int {f\left( x \right)dx} }$ and the relationship between F and A is $\boxed{F\left( x \right) = A\left( x \right) + C}.$

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Derivatives

Keywords: Derivative, function, differentiate, minimum value, F, anti-derivative, f, area, A, function, relationship, relation, integral, differentiation.