Question

The function f(x) = `x/2 + 2/x` has a local minima at x equal to ______.

Options

• 2

• 1

• 0

• −2

Answer 1

The function f(x) = `x/2 + 2/x` has a local minima at x equal to 2.

Explanation:

We have,

f(x) = `x/2 + 2/x`

f'(x) = `1/2-2/(x^2)`

Put, f'(x) = 0 ⇒ `1/2 - 2/(x^2) = 0`

⇒ `1/2 = 2/x^2`

⇒ x² = 4

⇒ x = ± 2

Now, f''(x) = `6/(x^3)`

At x = 2, f''(2) = `6/8 >0`

At x = −2, f''(−2) = `-6/8<0`

Thus, f(x) has local minima at x = 2