1. Let a, b R, a < b. Provide a complete and detailed proof of the...

Transcribed Image Text:

1. Let a, b R, a < b. Provide a complete and detailed proof of the following statement: If f is continuous on [a, b] and define F(x) = f f(t)dt, any x = [a,b], then F' (b) = f(b). That is that the left-hand derivative of F at x = b equals f(b). Do not use FTOCI. 1. Let a, b R, a < b. Provide a complete and detailed proof of the following statement: If f is continuous on [a, b] and define F(x) = f f(t)dt, any x = [a,b], then F' (b) = f(b). That is that the left-hand derivative of F at x = b equals f(b). Do not use FTOCI.

Answer rating: 100% (QA)

To prove the statement that if f is continuous on ab and Fx a x ftdt for any xab then F bfb we can use the fundamental theorem of calculus but since you requested not to use it we will employ an alter... View the full answer