A function f: \bo {R} \to \bo {R} is defined as f(x)=x^3+1. Then the function has

Correct Answer is : neither maximum value nor minimum value

both maximum and minimum values

CBSE Class 12 Math 2022 Term I Solved Paper - Question 3

Question : 3 of 50

Marks: +1, -0

A function

f: \bo {R} → \bo {R}

is defined as

f(x)=x^3+1

. Then the function has

Solution:

Explanation: Given,

f(x)=x^3+1

∴ \;f^{'}(x)\;=3 x^2 \;\text " and "\; f^{' '}(x)=6 x

\;\text " Put "\;\;f^{'}(x)\;=0

⇒ 3 x^2\;=0 ⇒ x=0

\;\;\text " At "\;\;x\;=0, f^{' '}(x)=0

Thus,

f(x)

has neither maximum value nor minimum value.

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