Question

The angle between the curves $y=x^2$ and $6y=7-x^3$ at the point (1, 1) is

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{2}$
• C. $ta{n}^{-1}\left(2\right)$
• D. $ta{n}^{-1}\left(\frac{5}{\sqrt{3}}\right)$

Answer 1

Answer: (B)

$\frac{\pi }{2}$

$y_1^{\prime }=2x$
$y_1^{\prime }{|}_{(1,1)}=2=m_1$
$6y_2^{\prime }=-3x^2$
$\Rightarrow y_2^{\prime }=\frac{-1}{2}{x}^2$
$y_2^{\prime }{|}_{(1,1)}=-\frac{1}{2}=m_2$
$m_1{m}_2=-1$
$\therefore$ angle between the curves is $\frac{\pi }{2}$