New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Application of Derivatives question

2008 · Shift 1 · Q45

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Advanced
Mathematics
Application of Derivatives
2008 · Shift 1 · Q45

Application of Derivatives question

2008 · Shift 1 · Q45

JEE AdvancedMathematicsApplication of DerivativesMCQ+3 / −1

The total number of local maxima and local minima of the function

f(x) = \left\{ {\begin{matrix} {{{(2 + x)}^3},} & { - 3 \lt x \le - 1} \\ {{x^{2/3}},} & { - 1 \lt x \lt 2} \\ \end{matrix} } \right.

is

A
0
B
1
C
2
D
3

More from Application of Derivatives

Let $f (x)$ be differentiable on the interval (0, $\infty$ ) such that $f (1) = 1$ , and $t \to x lim \frac{t ^{2} f ( x ) - x ^{2} f ( t )}{t - x} = 1$ for each $x > 0$ . Then $f (x)$ is2007 · MCQ
Let ℝ denote the set of all real numbers. Let f: ℝ → ℝ be defined by $f (x) = ⎩ ⎨ ⎧ \frac{6 x + sin x}{2 x + sin x}, \frac{7}{3}, if x e q 0, if x = 0.$ Then which of the following…2025 · Multiple correct
Let $Q$ be the cube with the set of vertices ${(x_{1}, x_{2}, x_{3}) \in R^{3} : x_{1}, x_{2}, x_{3} \in {0, 1}}$ . Let $F$ be the set of all twelve lines containing the diagonals of the six faces of the cube $Q$ . Let $S$ …2023 · MCQ
Let $α = k = 1 \sum \infty sin^{2 k} (\frac{π}{6})$ Let $g : [0, 1] \to R$ be the function defined by $g (x) = 2^{α x} + 2^{α (1 - x)} .$ Then, which of the following statements is/are…2022 · Multiple correct
Consider the rectangles lying the region ${(x, y) \in R \times R : 0 \leq x \leq \frac{π}{2}$ and $0 \leq y \leq 2 sin (2 x)}$ and having one side on the X-axis. The area of the rectangle…2020 · MCQ
Let f : R $\to$ R be given by $f (x) = (x - 1) (x - 2) (x - 5)$ . Define $F (x) = 0 \int x f (t) d t$ , x > 0 Then which of the following options is/are correct?2019 · Multiple correct
Let, $f (x) = \frac{s i n π x}{x ^{2}}$ , x > 0 Let x1 < x2 < x3 < ... < xn < ... be all the points of local maximum of f and y1 < y2 < y3 < ... < yn < ... be all the points of local minimum of f. Then…2019 · Multiple correct
For each positive integer n, let $y_{n} = \frac{1}{n} (n + 1) (n + 2) ... (n + n)^{\frac{1}{n}}$ . For x $\in$ R, let [x] be the greatest integer less than or equal to x. If $n \to \infty lim y_{n} = L$ , then the value…2018 · Numerical