Which of the following statements best explains why the line tangent to the curve at…

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Which of the following statements best explains why the line tangent to the curve

x^{2/3}+y^{2/3}=4

at the point

(0,2)

is vertical? (a) Because the curve is symmetric about the

y

-axis, any point with

x=0

must have a vertical tangent (b) Because the curve has a cusp at

(0,2)

, so no tangent line can be drawn (c) Because

\dfrac{dy}{dx}

is undefined at

(0,2)

due to division by zero, so the tangent line is vertical (d) Because

\dfrac{dy}{dx}=0

(0,2)

, giving a horizontal tangent