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NDA 2024

Exam: NDA
Year: 2024
Subject: Mathematics
Chapter: Functions

NDA 2024 · Mathematics · Functions

What is the minimum value of the function f(x)= _ 10 (x^2+2 x+11) ?

What is the minimum value of the function

f(x)=\log _{10}\left(x^2+2 x+11\right) ?

Options

A $0$
B $1$
C $2$
D $10$

Correct answer

B. $1$

Step-by-step solution

Given,

\mathrm{f}(\mathrm{x})=\log _{10}

\left(\mathrm{x}^2+2 \mathrm{x}+11\right)

For minimum and maximum

\begin{aligned} & f(x)=0 \\ & \frac{2 x+2}{x^2+2 x+11}=0 \quad\left(\sin , x^2+2 x+11>0\right) \end{aligned}

At,

x=-1

, we get minimum value of

f(x) f(-1)=\log _{10} 10=I

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