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Q.
The equation of the tangent to the curve $y = (4 - x^2)^{2/3}$ at $x = 2$ is
Application of Derivatives
Solution:
$ \frac{dy}{dx} = \frac{-4x}{3} \left(4 - x^{2}\right)^{-1/3}$
$\Rightarrow \left(\frac{dy}{dx}\right)_{\left(2, 0\right)} \to \infty$.
Hence there is a vertical tangent to the given curve at $x = 2$. Hence, the equation of the tangent at $x = 2$ is $x = 2$ (the vertical line through $(2,0)$).