AP EAMCET · Maths · Application of Derivatives
Find the absolute maximum of \(x^{40}-x^{20}\) on the interval \([0,1]\).
- A \(\frac{-1}{4}\)
- B 0
- C \(\frac{1}{4}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(B) 0
Step-by-step Solution
Detailed explanation
Let \[ \begin{aligned} f(x) & =x^{40}-x^{20} \\ f^{\prime}(x) & =40 x^{39}-20 x^{19} \\ f^{\prime}(x) & =0 \Rightarrow 20 x^{19}\left(2 x^{20}-1\right)=0 \\ x & =0, x=1 \\ f(0) & =0 \\ f(1) & =0 \end{aligned} \] \(\therefore\) Maximum value of \(x^{40}-x^{20}\) in \([0,1]\) is 0…
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