JEE Mains · Maths · STD 12 - 5. continuity and differentiation
The number of points, where the curve \(y=x^5-20 x^3+50 x+2\) crosses the \(x\)-axis, is \(............\).
- A \(4\)
- B \(3\)
- C \(5\)
- D \(1\)
Answer & Solution
Correct Answer
(C) \(5\)
Step-by-step Solution
Detailed explanation
\(y=x^5-20 x^3+50 x+2\) \(\frac{d y}{d x}=5 x^4-60 x^2+50=5\left(x^4-12 x^2+10\right)\) \(\frac{d y}{d x}=0 \Rightarrow x^4-12 x^2+10=0\) \(\Rightarrow x^2=\frac{12 \pm \sqrt{144-40}}{2}\) \(\Rightarrow x^2=6 \pm \sqrt{26} \Rightarrow x^2 \approx 6 \pm 5.1\)…
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
- Let \(L_1\) be the length of the common chord of the curves \(x^2 + y^2\, = 9\) and \(y^2\, = 8x\), and \(L_2\) be the length of the latus rectum of \(y^2\, = 8x\), thenJEE Mains 2014 Hard
- The plane which bisects the line segment joining the points \((-3, -3, 4)\) and \((3, 7, 6)\) at right angles, passes through which one of the following points?JEE Mains 2019 Hard
- The largest \(\mathrm{n} \in \mathrm{N}\) such that \(3^{\mathrm{n}}\) divides 50 ! is:JEE Mains 2025 Easy
- If \(A\) and \(B\) are two non-zero \(n \times n\) matrics such that \(A ^2+ B = A ^2 B\), thenJEE Mains 2023 Hard
- Let \(S_{1}: x^{2}+y^{2}=9\) and \(S_{2}:(x-2)^{2}+y^{2}=1\). Then the locus of center of a variable circle \(S\) which touches \(S_{1}\) internally and \(S_{2}\) externally always passes through the points :JEE Mains 2021 Hard
- Consider a triangular plot \(ABC\) with sides \(AB = 7\, m\), \(BC = 5\, m\) and \(CA = 6\, m\). A vertical lamp-post at the mid point \(D\) of \(AC\) subtends an angle \(30^o\) at \(B\). The height (in \(m\)) of the lamp-post isJEE Mains 2019 Hard
More PYQs from JEE Mains
- The function \(\mathrm{f}(\mathrm{x})\), that satisfies the condition \(\mathrm{f}(\mathrm{x})=\mathrm{x}+\int_{0}^{\pi / 2} \sin \mathrm{x} \cdot \cos y \mathrm{f}(\mathrm{y}) \mathrm{dy}\), is :JEE Mains 2021 Hard
- The total number or irrational terms in the binomial expansion of \(\left( {{7^{1/5}} - {3^{1/10}}} \right)^{60}\) isJEE Mains 2019 Hard
- The area (in sq. units) of the region enclosed between the parabola \(y ^{2}=2 x\) and the line \(x + y =4\) isJEE Mains 2022 Hard
- Let \( f(x)=\int\frac{(2-x^{2})e^{x}}{(\sqrt{1+x})(1-x)^{\frac{3}{2}}}dx \). If \( f(0)=0 \), then \( f(\frac{1}{2}) \) is equal to:JEE Mains 2026 Easy
- Let the system of linear equations \(x+y+k z=2\) ; \(2 x+3 y-z=1\) ; \(3 x+4 y+2 z=k\) , have infinitely many solutions. Then the system \(( k +1) x +(2 k -1) y =7\) ; \((2 k +1) x +( k +5) y =10 \text { has : }\)JEE Mains 2023 Hard
- Two players \(A\) and \(B\) play a series of games of badminton. The player, who wins \(5\) games first, wins the series. Assuming that no game ends in a draw, the number of ways, in which player \(A\) wins the series is __________.JEE Mains 2026 Medium