The point $P$ lies on the curve $y = 3x^{3} - 2x + a$, where $a$ is a constant. The equation o

Question

The point $P$ lies on the curve $y = 3x^{3} - 2x + a$, where $a$ is a constant. The equation of the tangent at $P$ is $9y = -9x + 43$. Find the coordinates of $P$, Given that the $x$-coordinate of $P$ is positive, find the value of $a$, the equation of the normal to the curve at $P$.

Accepted Answer

(a) $\left(\frac13,\frac{40}{9}\right)$ or $\left(-\frac13,\frac{46}{9}\right)$ (b) $a=5$ (c) $y=x+\frac{37}{9}$

Problems involving Tangents and Normals

Problems involving Tangents and Normals

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