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The angle of intersection of the curves $y = x^{2}, 6 y = 7 - x^{3}$ at $(1, 1)$ is

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π / 4

π / 3

π / 2

none of these

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detailed solution

Correct option is C

The two curves are $y = x^{2}$ and $6 y = 7 - x^{3} .$ These

two intersect at $(1, 1)$

Now,

$y = x^{2} \Rightarrow \frac{d y}{d x} = 2 x \Rightarrow m_{1} = {(\frac{d y}{d x})}_{{1, 1)} = 2$

and $6 y = 7 - x^{3} \Rightarrow \frac{d y}{d x} = - \frac{x^{2}}{2} \to m_{2} = {(\frac{d y}{d x})}_{(1, 1)} = - \frac{1}{2}$

Clearly $m_{1} m_{2} = - 1$

Thus, the angle of intersection of two curves is $π / 2$

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The angle of intersection of the curves y=x2,6y=7−x3 at (1,1) is