Let f:[-1, 2] → R be differentiable such that 0 ≤

Question

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 -2 ≤ f(2) – f(-1) ≤ 1	1 ≤ f(2) – f(-1) ≤ 2	- 3 ≤ f(2) – f(-1) ≤ 0	- 2 ≤ f(2) – f(-1) ≤ 0

Y RAJYALAKSHMI · Accepted Answer

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)

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

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

-2 ≤ f(2) – f(-1) ≤ 1

1 ≤ f(2) – f(-1) ≤ 2

- 3 ≤ f(2) – f(-1) ≤ 0

- 2 ≤ f(2) – f(-1) ≤ 0

Aditya Kartikeya , 10 Years ago

Y RAJYALAKSHMI

LIVE ONLINE CLASSES

The area of a square field is 640000cm².what is its area in hectares

integral calculus

Please solve this integration. I am facing difficulty in it
How to solve this. Please solve anyone. Humble request

integral calculus

Using laplace transform, solve d²y/dt²+ dy/dt = t² +2t given that y=4 and y’=-2 and t=0

integral calculus

how to solve this?
this is interger type question .

integral calculus

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

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 -2 ≤ f(2) – f(-1) ≤ 1 1 ≤ f(2) – f(-1) ≤ 2 - 3 ≤ f(2) – f(-1) ≤ 0 - 2 ≤ f(2) – f(-1) ≤ 0

Aditya Kartikeya , 10 Years ago

Y RAJYALAKSHMI

LIVE ONLINE CLASSES

Other Related Questions on integral calculus

The area of a square field is 640000cm2.what is its area in hectares

integral calculus

Please solve this integration. I am facing difficulty in it How to solve this. Please solve anyone. Humble request

integral calculus

Using laplace transform, solve d2y/dt2 + dy/dt = t2 +2t given that y=4 and y’=-2 and t=0

integral calculus

how to solve this?this is interger type question .

integral calculus

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

-2 ≤ f(2) – f(-1) ≤ 1

1 ≤ f(2) – f(-1) ≤ 2

- 3 ≤ f(2) – f(-1) ≤ 0

- 2 ≤ f(2) – f(-1) ≤ 0

The area of a square field is 640000cm².what is its area in hectares

Please solve this integration. I am facing difficulty in it
How to solve this. Please solve anyone. Humble request

Using laplace transform, solve d²y/dt²+ dy/dt = t² +2t given that y=4 and y’=-2 and t=0

how to solve this?
this is interger type question .