Practicing Success
Practicing Success
CUET Preparation Today
The condition $f(x)=x^3+p x^2+q x+r(x \in R)$ to have no extreme value, is |
$p^2<3 q$ $2 p^2<q$ $p^2<\frac{q}{4}$ $p^2>3 q$ |
$p^2<3 q$ |
If $f(x)=x^3+p x^2+q x+r$ has no extreme values, then $f'(x) \neq 0$ for any $x \in R$ $\Rightarrow 3 x^2+2 p x+q \neq 0$ for any $x \in R$ $\Rightarrow 3 x^2+2 p x+q=0$ has no real root $\Rightarrow 4 p^2-12 q<0 \Rightarrow p^2<3 q$. |
