Mathematics

The angle made by the tangent line at (1, 3) on the curve $$y=4x-{ x }^{ 2 }$$ with $$\overline{ OX } $$ is 


ANSWER

$$\tan ^{-1}2$$


SOLUTION
Given,

$$y=4x-x^2$$

$$\dfrac{dy}{dx}=4-2x$$

$$\dfrac{dy}{dx}_{(1,3)}=4-2(1)=2$$

Therefore, angle made by tangent,

$$\tan \theta =2$$

$$\therefore \theta =\tan ^{-1}2$$
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Single Correct Medium Published on 17th 09, 2020
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