Flag Integral Calculus> Let f:[-1, 2] → R be differentiable such ...
question mark

Let f:[-1, 2] → R be differentiable such that 0 ≤ f’(t) ≤ 1 for t ∈ [-1, 0] and -1 ≤ f’(t) ≤ 0 for t ∈ [0, 2]. Then
options
  1. -2 ≤ f(2) – f(-1) ≤ 1
  2. 1 ≤ f(2) – f(-1) ≤ 2
  3. - 3 ≤ f(2) – f(-1) ≤ 0
  4. - 2 ≤ f(2) – f(-1) ≤ 0

Aditya Kartikeya , 10 Years ago
Grade 10
anser 1 Answers
Y RAJYALAKSHMI

Last Activity: 10 Years ago

Property: If m & M are the minimum and  maximum values of f(x) in [a, b], then ∫ f( x) between the limits a & b lies between m(b – a ) & M(b – a)
 
0 ≤ f ’ (t) ≤ 1 for  –1 ≤ t ≤ 0
=>f (t) =  ∫ f ‘ (t) between the limits -1 & 0  = f (0) – f (–1) 
By using above property we have 
0(0 + 1) ≤ f (0) – f (–1) ≤ 1( 0 + 1)
=> 0 ≤ f (0) – f (–1) ≤ 1  -------------- (1)
– 1 ≤ f ’ (t) ≤ 0 for  0 ≤ t ≤ 2
=>f (t) =  ∫ f ‘ (t) between the limits 0 & 2  = f (2) – f (0) 
By using above property we have 
–1(2 – 0) ≤ f (2) – f (0) ≤ 0( 2 – 0)
=> –2 ≤ f (2) – f (0) ≤ 0  -------------- (1)
Adding (1) & (2), we get
–2 ≤ f (2) – f (– 1) ≤ 1
 
Ans: –2 ≤ f (2) – f (– 1) ≤ 1  – Option (1)

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments