AP EAMCET · Maths · Application of Derivatives
The sum of the global minimum and global maximum values of the function \(f(x)=\frac{4}{3} x^3-4 x\) in \([0,2]\) is
- A \(0\)
- B \(8 / 3\)
- C \(-8 / 3\)
- D \(1\)
Answer & Solution
Correct Answer
(A) \(0\)
Step-by-step Solution
Detailed explanation
Given \(f(x)=\frac{4}{3} x^3-4 x, x \in[0,2]\) Now, \(\mathrm{f}^{\prime}(\mathrm{x})=0 \Rightarrow 4 \mathrm{x}^2-4=0 \Rightarrow \mathrm{x}= \pm 1\) Now \(\mathrm{f}(0)=0, \mathrm{f}(1)=\frac{4}{3}-4=-\frac{8}{3}=\) global min \(f(-1)=\frac{-4}{3}+4=\frac{8}{3}\)…
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