WBJEE · Maths · Functions
If \(f(x)\) is an odd differentiable function defined on \((-\infty, \infty)\) such that \(f^{\prime}(3)=2,\) then \(f^{\prime}(-3)\) is equal to
- A 0
- B 1
- C 2
- D 4
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
Given that \(f(x)\) is an odd differentiable function. Then, \(f(-x)=-f(x)\) \(\begin{array}{lr}\Rightarrow & -f^{\prime}(-x)=-f^{\prime}(x) \\ \Rightarrow & f^{\prime}(-x)=f^{\prime}(x)\end{array}\) Put \(x=3\) in Eq. (i), we get \(\therefore\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \((\alpha+\sqrt{\beta})\) and \((\alpha-\sqrt{\beta})\) are the roots of the equation \(x^{2}+p x+q=0,\) where \(\alpha, \beta, p\) and \(q\) are real, then the roots of the equation \(\left(p^{2}-4 q\right)\left(p^{2} x^{2}+4 p x\right)-16 q=0\) areWBJEE 2012 Medium
- The expression \(a x^{2}+b x+c(a, b\) and \(c\) are real \()\) has the same sign as that of a for all \(x\) ifWBJEE 2020 Easy
- A double ordinate \(\mathrm{PQ}\) of the hyperbola \(\frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}-\frac{\mathrm{y}^{2}}{\mathrm{~b}^{2}}=1\) is such that \(\Delta \mathrm{OPQ}\) is equilateral, \(\mathrm{O}\) being the centre of the hyperbola. Then the eccentricity e satisfies the relationWBJEE 2020 Easy
- \(\lim _{x \rightarrow 0^{+}}\left(e^{x}+x\right)^{1 / x}\)WBJEE 2019 Medium
- The co-ordinate of a point on the auxiliary circle of the ellipse \(x^{2}+2 y^{2}=4\) corresponding to the point on the ellipse whose eccentric angle is \(60^{\circ}\) will beWBJEE 2021 Easy
- If \(z_1, z_2\) are complex numbers such that \(\frac{2 z_1}{3 z_2}\) is a purely imaginary number, then the value of \(\left|\frac{z_1-z_2}{z_1+z_2}\right|\) isWBJEE 2025 Medium
More PYQs from WBJEE
- Which of the following compounds is not formed in iodoform reaction of acetoneWBJEE 2011 Hard
- Two decks of playing cards are well shuffled and 26 cards are randomly distributed to a player. Then, the probability that the player gets all distinct cards isWBJEE 2012 Easy
- The integrating factor of the differential equation \(\frac{d y}{d x}+\left(3 x^{2} \tan ^{-1} y -x^{3}\right)\left(1+y^{2}\right)=0\) isWBJEE 2015 Medium
- \(360 \mathrm{~cm}^3\) of a hydrocabon diffuses in 30 minutes, while under the same conditions \(360 \mathrm{~cm}^3\) of \(\mathrm{SO}_2\) gas diffuses in one hour. The molecular formula of the hydrocabon isWBJEE 2025 Medium
- A block of mass \(m(=0.1 \mathrm{kg})\) is hanging over a frictionless light fixed pulley by an inextensible string of negligible mass. The other end of the string is pulled by a constant force \(F\) in the vertically downward direction. The linear momentum of the block increases by \(2 \mathrm{kgms}^{-1}\) in \(1 \mathrm{s}\) after the block starts from rest. Then, (given \(g=10 \mathrm{ms}^{-2}\) )
WBJEE 2013 Medium - If \(x \sin \left(\frac{y}{x}\right) d y=\left[y \sin \left(\frac{y}{x}\right)-x\right] d x, x>0\) and \(y(1)=\frac{\pi}{2}\) then the value of \(\cos \left(\frac{y}{x}\right)\) isWBJEE 2020 Medium