Math CentralQuandaries & Queries


Question from Kevin, a student:

Given that the curve y=x^3 has a tangent line that passes through point (0,2). Find the equation of the tangent line

Hi Kevin,

There is a point $P$ on the curve $y = x^3$ where the tangent to $y = x^3$ at $P$ passes through (0,2). Suppose the x-coordinate of $P$ is $a$ then since $P$ is on the graph of $y = x^3$ the y-coordinate of $P$ is $a^3.$ Use calculus to find the slope of the tangent to $y = x^3$ at $P$ and write the equation of the tangent. This tangent line passes through (0,2). Solve for $a.$ Make sure you verify your answer.


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