24/7 Homework Help

Essaynice Will Help You Write Your Essays and Term Papers

From initial topic to finished paper

Answered » You can buy a ready-made answer or pick a professional tutor to order an original one.

Assignment help 3377

by | Apr 10, 2023 | Posted Assignments

Hi tutor, can you please help me to solve that question and show all the work?

Let f (x) be a function on (0, 100), having derivative f ? (x) and a primitive function F (x) = x f (t)dt 0

defined on the same domain. For all x ? (0,100), it is known that f(x) ? 0 and f?(x) ? 0.

(a)we learned that f?(x) ? 0 for all x ? (0,100) implies that f(x) is decreasing. Prove this statement by using the properties of definite integrals. In other words, for all a,b ? (0,100), prove that f(a) ? f(b) if a < b.

(b) we also learned that F??(x) = f?(x) ? 0 for all x ? (0,100) implies that F(x) is concave. Prove this statement by using the properties of definite integrals and results from (a). In other words, for all a, b ? (0, 100)

prove that : F ((a+b)/2) ? 1/2 (F(a)+F(b))

HOME TO CERTIFIED WRITERS

Why Place An Order With Us?

  • Certified Editors
  • 24/7 Customer Support
  • Profesional Research
  • Easy to Use System Interface
  • Student Friendly Pricing

Have a similar question?

PLAGIRAISM FREE PAPERS

All papers we provide are well-researched, properly formatted and cited.

TOP QUALITY

All papers we provide are well-researched, properly formatted and cited.

HIGHLY SECURED

All papers we provide are well-researched, properly formatted and cited.

Order-Essaynice
Open chat
1
Powered by Essaynice
Hello! Welcome to to our WhatsApp support.
We offer READY solutions, HIGH QUALITY PLAGIARISM FREE essays and term-papers.

We are online and ready to help.