Question

of minima
of
Find
the point
y = x3 – 12x – 5​

Answer 1

Answer:

The given equation of curve is

y = x3 - 12x+18

∴ dy/dx = 3x2-12

If tangents to the curve are parallel to the x-axis

∴ dy/dx = 0

⇒ 3x2-12 =0

⇒ x2 = 12/3 = 4

∴ x = ± 2

For x = 2, y = 23 - 12 × 2 + 18 = 2

and for x = -2, y =(-2)3 - 12(-2) + 18 = 34

So, the points are (2,2) and (-2,34).