Question

22. y = 3x2 + 12x + 4 find dy/dx​

Answer 1

Answer:

Solution:

Given

y = 2x3 + 3x2 - 12x + 2 --- (1)

Differentiate equation (1) w.r.t., x

dy/dx = 6x2 + 6x - 12 --- (2)

Equation (2) is ‘slope if tangent at any point’.

Since the tangent is horizontal, its slope is zero.

∴ 6x2 + 6x - 12 = 0

x2 + x - 2 = 0

(x + 2)(x - 1) = 0

∴ The roots are x = -2 and x = 1

When x = -2,

y = 2(-2)3 +3(-2)2 -12(-2) + 2

y = -16 + 12 + 24 + 2

y = 22

When x = 1,

y = 2(1)3 + 3(1)2 -12(1) + 2

y = 2 + 3 - 12 + 2

y = -5

Therefore, required points are (-2, 22) and (1, -5)