Let f(x)=2 cos -1 x+4 cot -1 x-3 x2-2 x+10, x ∈[- 1,1]. If [ a , b ] is the range of the function then 4 a - b is equal to:

Question

Let f(x)=2 cos -1 x+4 cot -1 x-3 x2-2 x+10, x ∈[- 1,1]. If [ a , b ] is the range of the function then 4 a - b is equal to: (A) 11 (B) 11-π (C) 11+π (D) 15-π

Tardigrade Admin · Accepted Answer

f prime(x)=(-2/√1-x2)-(4/1+x2)-6 x-2 =-2[(1/√1-x2)+(2/1+x2)+3 x+1] f prime(x)<0 ⇒ f(x) is a dec. function f(1)=π+5 f(-1)=5 π+5 Range: [a,b] =[π+5,5 π+5] a =π+5, b=5 π+5 ⇒ 4 a-b=11-π

Q. Let $f (x) = 2 cos^{- 1} x + 4 cot^{- 1} x - 3 x^{2} - 2 x + 10, x \in [- 1, 1]$ . If $[a, b]$ is the range of the function then $4 a -$ $b$ is equal to:

$11$

$11 - π$

$11 + π$

$15 - π$

Q. Let f(x)=2cos−1x+4cot−1x−3x2−2x+10,x∈[−1,1]. If [a,b] is the range of the function then 4a− b is equal to:

11

11−π

11+π

15−π

f′(x)=1−x2​−2​−1+x24​−6x−2 =−2[1−x2​1​+1+x22​+3x+1] f′(x)<0⇒f(x) is a dec. function f(1)=π+5 f(−1)=5π+5 Range : [a,b]=[π+5,5π+5] a=π+5,b=5π+5⇒4a−b=11−π

Q. Let $f (x) = 2 cos^{- 1} x + 4 cot^{- 1} x - 3 x^{2} - 2 x + 10, x \in [- 1, 1]$ . If $[a, b]$ is the range of the function then $4 a -$ $b$ is equal to:

$11$

$11 - π$

$11 + π$

$15 - π$