Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-Minima- Word problemsMedium2 minQB

MathematicsMediumsingle choice

The largest area of the rectangle which has one side on the X-axis and two vertices on the curve $y = e^{- x^{2}}$ is

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Answer:

Solution:

Let $f (t) = t e^{- t^{2}}$ $f^{1} (t) = - 2 t^{2} e^{- t^{2}} + e^{- t^{2}} = e^{- t^{2}} (1 - 2 t^{2}) f^{1} (t) = 0 \Rightarrow t = \frac{1}{2}$ Max area $= 2 \times \frac{1}{2} \times e^{\frac{- 1}{2}} = \frac{2}{e}$

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Maxima-Minima- Word problems

⏱ 2mℹ️ Source: QB

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