Answer:
(1,2) (-1,-2)
Step-by-step explanation:
Given the equation of curve as y= 2x³ and slope of tangent line as 6 then
Find dy/dx
[tex]\frac{d}{dx} (y)=\frac{d}{dx}(2x^3)[/tex]
Apply the power rule
[tex]\frac{d}{dx} (x^n)=nx^{n-1}[/tex]
where n=constant
Hence, our equation will be;
[tex]\frac{dy}{dx} =2*3x^{3-1} \\\\\\\frac{dy}{dx} =6x^{2}[/tex]
But you know that dy/dx=slope=6
6x²=6--------------------divide both sides by 6
6x²/6=6/6
x²=1
x=√1=±1
x=1 and -1
Remember y=2x³
Substitute value of x to get value of y
y=2x³
y=2×1³
y=2×1=2
y=2
For x=-1, find y coordinate
y=2×-1³=2×-1=-2
coordinate will be (-1,-2)
Coordinates of the points will be (1,2) ,(-1,-2)
