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Find the points on the curve y = x^3 at which the slope of the

Question

Find the points on the curve $y = x^{3}$ at which the slope of the tangent is equal to the $y$ coordinate of the point.

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Emma Discussed

Find the points on the curve

y = x^{3}

at which the slope of the tangent is equal to the

y

coordinate of the point.

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

The equation of the given curve is

y = x^{3}

∴ \frac{d y}{d x} = 3 x^{2}

When the slope of the tangent is equal to the

y

-coordinate of the point,

then

\frac{d y}{d x} = y = 3 x^{2}

Also, we have

y = x^{3}

3 x^{2} = x^{3} \Rightarrow x^{2} (x - 3) = 0 \Rightarrow x = 0, x = 3

When

x = 0

, then

y = 0

and when

x = 3

, then

y = 3 (3)^{2} = 27

Hence, the required points are

(0, 0)

and

(3, 27) .

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Question Text	Find the points on the curve $y = x^{3}$ at which the slope of the tangent is equal to the $y$ coordinate of the point.
Answer Type	Text solution:1
Upvotes	150