A curve has the equation $y = ax^3 - 2x + c$, where $a$ and $c$ are constants. Given that

Question

A curve has the equation $y = ax^3 - 2x + c$, where $a$ and $c$ are constants. Given that the gradient of the curve at the point $(1, 1)$ is $4$, find the values of $a$ and $c$. Hence find the coordinates of all other points on the curve where the gradient of the curve is $4$, and the range of values of $x$ where the gradient of the curve is positive.

Accepted Answer

(i) $a=2,\ c=1$ (ii) $(-1,1)$ (iii) $x\dfrac{\sqrt3}{3}$

Applications of Differentiation - Derivative as the Gradient of a Curve

Applications of Differentiation - Derivative as the Gradient of a Curve

Video Solution:

Solution:

Solution locked