Suppose f(x) is continuous everywhere and F(x) = integral_0^x f(t)dt. Which of t
ID: 2879327 • Letter: S
Question
Suppose f(x) is continuous everywhere and F(x) = integral_0^x f(t)dt. Which of the following is true. i.e. the statement reason given. y = F(x) is differentiable everywhere because of the Mean Value Theorem. y = F(x) is continuous everywhere because F(x) has a derivative by the Fundamental Theorem of the Calculus and differentiable functions are continuous. y = F(x) is continuous because the Intermediate Value Theorem proves the integral of a continuous function is continuous. y = F(x) has a derivative because the chain rule implies the integral of a continuous function has a derivative. The function y = F(x) does not have a derivative because it is an integral.Explanation / Answer
Option (B) is correct
y = F (x) is continuous everywhere because F (x) has a derivative by the fundamental Theorem of calculus and differentiable function are continuous