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.

Penny