For what value of 'x' will the function y = x² - 4x have the maximum or minimum value?

Question

Question

This question was previously asked in

DFCCIL Executive S&T 29 Sept 2021 Official Paper

Answer 1

Concept used:

dy/dx = 0, the value of x gives the minimum value when d2y/dx2 is greater than 0, and gives the maximum value when d2y/dx2 is less than 0

Calculation:

y = x2 - 4x ----(i)

Differentiating (i),

dy/dx = 0

⇒ 2x - 4 = 0 ----(ii)

⇒ x = 2

By double differentiating equation (ii),

d2y/dx2 = 2 > 0

That means the minimum value of equation (i) is at x = 2

The minimum value of equation (i)

⇒ 2² - 4 × 2

⇒ -4

∴ The minimum value is at x = 2.