1
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The function $f(x)=2 x^3-3 x^2-12 x+4, x \in \mathbb{R}$ has

A
two points of local maximum.
B
two points of local minimum.
C
one local maximum and one local minimum.
D
neither maximum nor minimum.
2
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $\phi(x)=f(x)+f(2 a-x), x \in[0,2 a]$ and $f^{\prime \prime}(x)>0$ for all $x \in[0, a]$. Then $\phi(x)$ is

A
increasing on $[0, a]$.
B
decreasing on $[0, a]$.
C
increasing on $[0,2 a]$.
D
decreasing on $[0,2 a]$.
3
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $f$ be a function which is differentiable for all real $x$. If $f(2)=-4$ and $f^{\prime}(x) \geq 6$ for all $x \in[2,4]$, then

A
$f(4)<8$
B
$f(4) \geq 12$
C
$f(4) \geq 8$
D
$f(4)<12$
4
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha \log |x|+\beta x^2+x,(x \neq 0)$, then

A
$\alpha=-6, \beta=\frac{1}{2}$
B
$\alpha=-6, \beta=-\frac{1}{2}$
C
$\alpha=2, \beta=-\frac{1}{2}$
D
$\alpha=2, \beta=\frac{1}{2}$
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