1
GATE CSE 2025 Set 1
Numerical
+1
-0

Consider the given function $f(x)$.

$$f(x)=\left\{\begin{array}{cc} a x+b & \text { for } x<1 \\ x^3+x^2+1 & \text { for } x \geq 1 \end{array}\right.$$

If the function is differentiable everywhere, the value of $b$ must be _________ (Rounded off to one decimal place)

Your input ____
2
GATE CSE 2024 Set 2
MCQ (Single Correct Answer)
+1
-0.33

Let $f(x)$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$ such that

$f(x) = 1 - f(2 - x)$

Which one of the following options is the CORRECT value of $\int_0^2 f(x) dx$?

A

0

B

1

C

2

D

-1

3
GATE CSE 2024 Set 1
MCQ (Single Correct Answer)
+1
-0.33

Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be a function such that $f(x) = \max \{x, x^3\}, x \in \mathbb{R}$, where $\mathbb{R}$ is the set of all real numbers. The set of all points where $f(x)$ is NOT differentiable is

A

{-1, 1, 2}

B

{-2, -1, 1}

C

{0, 1}

D

{-1, 0, 1}

4
GATE CSE 2023
MCQ (More than One Correct Answer)
+1
-0

Let $$f(x) = {x^3} + 15{x^2} - 33x - 36$$ be a real-valued function. Which of the following statements is/are TRUE?

A
$$f(x)$$ does not have a local maximum.
B
$$f(x)$$ has a local maximum.
C
$$f(x)$$ does not have a local minimum.
D
$$f(x)$$ has a local minimum.
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