Question

The function f(x) = x² - 4x, x ∈ [0, 4] attains minimum value at
1. x = 0
2. x = 1
3. x = 2
4. x = 4
5. None of these

Answer 1

Correct Answer - Option 3 : x = 2

Concept:

Following steps to finding maxima and minima using derivatives:

Step-1: Find the derivative of the function.

Step-2: Set the derivative equal to 0 and solve. This gives the values of the maximum and minimum points.

Step-3: Now we have to find the second derivative.

Case-1: If f"(x) is less than 0 then the given function is said to be maxima

Case-2: If f"(x) Is greater than 0 then the function is said to be minima

Calculation:

Given:

f(x) = x² - 4x

Differentiating with respect to x, we get

⇒ f'(x) = 2x - 4

For minimum value, f'(x) = 0

⇒ 2x - 4 = 0

∴ x = 2

Again differentiating with respect to x, we get

⇒ f"(x) = 2 > 0

Hence f(x) attains minimum value at x = 2