TS EAMCET · Maths · Application of Derivatives
If \(m\) and \(M\) are respectively the absolute minimum and absolute maximum values of a function \(f(x)=2 x^3+9 x^2+12 x+1\) defined on \([-3,0]\), then \(m+M=\)
- A \(-7\)
- B \(0\)
- C \(1\)
- D \(5\)
Answer & Solution
Correct Answer
(A) \(-7\)
Step-by-step Solution
Detailed explanation
\(f^{\prime}(x)=6 x^2+18 x+12=6(x+2)(x+1)\) Critical points are \(x=-1, x=-2\) \(\begin{aligned} & f(-3)=-54+81-36+1=-8 \\ & f(-2)=-16+36-24+1=-3 \\ & f(-1)=-2+9-12+1=-4 ;(0)=1 \\ & m=-8, M=1 \Rightarrow M+m=-7 . \end{aligned}\)
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