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TS EAMCET · Maths · Application of Derivatives

If the absolute maximum and absolute minimum values of the function. \(f(x)=x^3-2 x^2+x-3\) defined on \([0,2]\) are \(\mathrm{M}\) and \(\mathrm{m}\) respectively, then \(\mathrm{M}+\mathrm{m}=\)

  1. A -4
  2. B \(\frac{-104}{27}\)
  3. C 2
  4. D -2
Verified Solution

Answer & Solution

Correct Answer

(A) -4

Step-by-step Solution

Detailed explanation

\(f(x)=x^3-2 x^2+x-3\) \( f^{\prime}(x)=3 x^2-4 x+1 \) \( \begin{aligned} & f^{\prime}(x)=0 \Rightarrow 3 x^2-4 x+1=0 \\ & \Rightarrow 3 x^2-3 x-x+1=0 \Rightarrow(3 x-1)(x-1)=0 \\ & \therefore \quad x=\frac{1}{3}, 1 \end{aligned} \)…