Question

Given function $f\left(x\right)=x^2+bx+c$; where $bandc$ are arbitrary constant. Choose the correct statement.

• A. $f\left(x\right)$ is a periodic function
• B. $f\left(x\right)$ is a quadratic function
• C. $f\left(x\right)$ has a minima at a single value of $x$
• D. $f\left(x\right)$ has a maxima at a single value of $x$

Answer 1

Answer: (B), (C)

$f\left(x\right)$ is a quadratic function
$f\left(x\right)$ has a minima at a single value of $x$

Given equation is $f\left(x\right)=x^2+bx+c$

As it is a polynomial in degree 2, it is a quadratic equation

Differentiating the equation and equating to 0 for obtaining minima

$\Rightarrow 2x+b=0$

$\Rightarrow x=-b/2$

$\therefore$minima occur at single value of $x$