Question -
Answer -
Given the curve y = x3 – 2x2 –2x and a line y = 2x – 3
First, we will find the slope of tangent
y = x3 – 2x2 – 2x
y = 2x – 3 is the form of equation of a straight liney = mx + c, where m is the Slope of the line.
So the slope of the line is y = 2 × (x) – 3
Thus, the Slope = 2. … (2)
From (1) & (2)
⇒ 3x2 –4x – 2 = 2
⇒ 3x2 –4x = 4
⇒ 3x2 –4x – 4 = 0
We will use factorization method to solve the above Quadraticequation.
⇒ 3x2 –6x + 2x – 4 = 0
⇒ 3x (x – 2) + 2 (x – 2) = 0
⇒ (x– 2) (3x + 2) = 0
⇒ (x– 2) = 0 & (3x + 2) = 0
⇒ x= 2 or
x = -2/3
Substitute x = 2 & x = -2/3 in y = x3 –2x2 – 2x
When x = 2
⇒ y= (2)3 – 2 × (2)2 – 2 × (2)
⇒ y= 8 – (2 × 4) – 4
⇒ y= 8 – 8 – 4
⇒ y= – 4
