Page 1 of 1
Suppose F, G are continuous on [a, b], differentiable on (a,b) and that F'(x) = G'(x) for all 2 € (a,b). Using FTC, show
Posted: Thu May 12, 2022 10:47 am
by answerhappygod
- Suppose F G Are Continuous On A B Differentiable On A B And That F X G X For All 2 A B Using Ftc Show 1 (12.84 KiB) Viewed 39 times
Suppose F, G are continuous on [a, b], differentiable on (a,b) and that F'(x) = G'(x) for all 2 € (a,b). Using FTC, show that F and G differ by a constant. That is, show that there exists a C e R such that F(X) - G(2) = C. (Hint: Consider the function H = F G then use FTC to show that H is constant on [a, b].)