Question

A function f : R `rightarrow` R is defined as f(x) = x³ + 1. Then the function has ______.

Options

• no minimum value

• no maximum value

• both maximum and minimum values

• neither maximum value nor minimum value

Answer 1

A function f : R `rightarrow` R is defined as f(x) = x³ + 1. Then the function has neither maximum value nor minimum value.

Explanation:

Given, f(x) = x³ + 1

∴ f'(x) = 3x² and f"(x) = 6x

Put f'(x) = 0

`\implies` 3x² = 0 `\implies` x = 0

At x = 0, f"(x) = 0

Thus, f(x) has neither maximum value nor minimum value.