AP EAMCET · Maths · Application of Derivatives
If \(m\) and \(M\) respectively denote the minimum and maximum of \(f(x)=(x-1)^2+3\) for \(x \in[-3,1]\), then the ordered pair \((m, M)\) is equal to
- A \((-3,19)\)
- B \((3,19)\)
- C \((-19,3)\)
- D \((-19,-3)\)
Answer & Solution
Correct Answer
(B) \((3,19)\)
Step-by-step Solution
Detailed explanation
Given that, \[ f(x)=(x-1)^2+3, \quad x \in[-3,1] \] On differentiating w.r.t. \(x\), we get \[ f^{\prime}(x)=2(x-1) \] For maxima and minima, put \(f^{\prime}(x)=0\) \[ \begin{aligned} \Rightarrow & & 2(x-1) & =0 \\ \Rightarrow & & x & =1 \end{aligned} \] Now,…
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