The equation of the tangent to the curve y = (4 - x2)2/3 at x = 2 is

Question

The equation of the tangent to the curve y = (4 - x2)2/3 at x = 2 is (A) x = -2 (B) x = 2 (C) y = 2 (D) y = - 1

Tardigrade Admin · Accepted Answer

(dy/dx) = (-4x/3) (4 - x2)-1/3 ⇒ ((dy/dx))(2, 0) → ∞. 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)).

Q. The equation of the tangent to the curve $y = (4 - x^{2})^{2/3}$ at $x = 2$ is

$x = - 2$

$x = 2$

$y = 2$

$y = - 1$

$\frac{d y}{d x} = \frac{- 4 x}{3} (4 - x^{2})^{- 1/3}$
$\Rightarrow (\frac{d y}{d x})_{(2, 0)} \to \infty$ .
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 $(2, 0)$ ).

Q. The equation of the tangent to the curve y=(4−x2)2/3 at x=2 is

x=−2

x=2

y=2

y=−1