Question

At x = 0, f(x) = 2x² + 1 has 
1. Maximum
2. Minimum
3. Niether maximum nor minimum
4. Point of inflection

Answer 1

Correct Answer - Option 2 : Minimum

Concept:

Following steps to finding maxima and minima using derivatives.

Find the derivative of the function.

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

Now we have to find the second derivative.

• f"(x) is less than 0 then the given function is said to be maxima
• If f"(x) Is greater than 0 then the function is said to be minima

 

Calculation:

Given: f(x) = 2x² + 1 

Differentiation with respect to x

⇒ f'(x) = 4x

For maxima and minima;

⇒ f'(x) = 0

⇒ 4x = 0

⇒ x =  0

Again differentiation with respect to x

⇒ f''(x) = 4

⇒ f''(0) = 4 > 0

So, x = 0 is the point of minimum

Hence, option 2 is correct