JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
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
- A \(11\)
- B \(11-\pi\)
- C \(11+\pi\)
- D \(15-\pi\)
Answer & Solution
Correct Answer
(B) \(11-\pi\)
Step-by-step Solution
Detailed explanation
\(f^{\prime}(x)=\frac{-2}{\sqrt{1-x^{2}}}-\frac{4}{1+x^{2}}-6 x-2\) \(=-2\left[\frac{1}{\sqrt{1-x^{2}}}+\frac{2}{1+x^{2}}+3 x+1\right]\) \(f^{\prime}(x)<0 \Rightarrow f(x)\) is a dec. function \(f(1)=\pi+5\) \(f(-1)=5 \pi+5\) Range : \([ a , b ] \equiv[\pi+5,5 \pi+5]\)…
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