JEE Main 2020 — Application Of Derivatives Question with Solution
From: JEE Main 2020 (Online) 7th January Morning Slot
Question
Let the function, ƒ:[-7, 0]R be continuous on [-7,0] and differentiable on (-7, 0). If ƒ(-7) = -
3 and ƒ'(x) 2, for all x (-7,0), then for all such functions ƒ, ƒ(-1) + ƒ(0) lies in the interval:
Choose an option
Show full solutionCorrect option: B
Correct answer
B
Step-by-step explanation
Using Lagrange’s Mean Value Theorem in [–7, –1]
= f'(c1)
As ƒ'(x) 2 then f'(c1) 2
2
2
f(-1) 9
Using Lagrange’s Mean Value Theorem in [–7, 0]
2
f(0) 11
ƒ(-1) + ƒ(0) 11 + 9
ƒ(-1) + ƒ(0) 20
= f'(c1)
As ƒ'(x) 2 then f'(c1) 2
2
2
f(-1) 9
Using Lagrange’s Mean Value Theorem in [–7, 0]
2
f(0) 11
ƒ(-1) + ƒ(0) 11 + 9
ƒ(-1) + ƒ(0) 20
Practice this on the real CBT interface
Solve this JEE Main question (and the rest of the Application Of Derivatives chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.
Solve interactively →About this question
This is a previous-year question from JEE Main 2020, covering the Application Of Derivatives chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.