WB JEE 2025 | Application of Derivatives Question 16 | Mathematics

WB JEE 2025

MCQ (Single Correct Answer)

-0.25

Let $p(x)$ be a real polynomial of least degree which has a local maximum at $x=1$ and a local minimum at $x=3$. If $p(1)=6$ and $p(3)=2$, then $p^{\prime}(0)$ is equal to :

WB JEE 2025

MCQ (Single Correct Answer)

-0.25

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

two points of local maximum.

two points of local minimum.

one local maximum and one local minimum.

neither maximum nor minimum.

WB JEE 2025

MCQ (Single Correct Answer)

-0.25

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

increasing on $[0, a]$.

decreasing on $[0, a]$.

increasing on $[0,2 a]$.

decreasing on $[0,2 a]$.

WB JEE 2025

MCQ (Single Correct Answer)

-0.25

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

$f(4)<8$

$f(4) \geq 12$

$f(4) \geq 8$

$f(4)<12$

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