JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f(x)=x^3+x^2 f^{\prime}(1)+x f^{\prime \prime}(2)+f^{\prime \prime \prime}(3), x \in R\) Then \(f^{\prime}(10)\) is equal to ..............
- A \(109\)
- B \(106\)
- C \(103\)
- D \(202\)
Answer & Solution
Correct Answer
(D) \(202\)
Step-by-step Solution
Detailed explanation
\( f(x)=x^3+x^2 \cdot f^{\prime}(1)+x \cdot f^{\prime \prime}(2)+f^{\prime \prime \prime}(3) \) \( f^{\prime}(x)=3 x^2+2 x f^{\prime}(1)+f^{\prime \prime}(2) \) \( f^{\prime \prime}(x)=6 x+2 f^{\prime}(1) \) \( f^{\prime \prime \prime}(x)=6\)…
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 the volume of a spherical ball is increasing at the rate of \(4 \pi \, cc/sec\), then the rate of increase of its radius (in \(cm/sec\)), when the volume is \(288 \pi \, cc\)JEE Mains 2014 Hard
- Let the point, on the line passing through the points \(P(1,-2,3)\) and \(Q(5,-4,7)\), farther from the origin and at a distance of \(9\) units from the point \(\mathrm{P}\), be \((\alpha, \beta, \gamma)\). Then \(\alpha^2+\beta^2+\gamma^2\) is equal to :JEE Mains 2024 Medium
- If the sum of the first four terms of an A.P. is 6 and the sum of its first six terms is 4, then the sum of its first twelve terms isJEE Mains 2026 Hard
- If the system of equations \(x+y+z=2\) \(2 x+4 y-z=6\) \(3 x+2 y+\lambda z=\mu\) has infinitely many solutions, thenJEE Mains 2020 Medium
- If \(f(x)=\left\{\begin{array}{ll}{\frac{\sin (a+2) x+\sin x}{x}} & {; x<0} \\ {b} & {; x=0} \\ {\frac{\left(x+3 x^{2}\right)^{\frac{1}{3}}-x^{\frac{1}{3}}}{x^{\frac{4}{3}}}} & {; x>0}\end{array}\right.\) is continuous at \(x=0,\) then \(a+2 b\) is equal toJEE Mains 2020 Hard
- Let \(\mathrm{A}=\)\(\left\{\theta \in[0,2 \pi]: 1+10 \operatorname{Re}\left(\frac{2 \cos \theta+i \sin \theta}{\cos \theta-3 i \sin \theta}\right)=0\right\} .\)
Then \(\sum_{\theta \in A} \theta^2\) is equal toJEE Mains 2025 Medium
More PYQs from JEE Mains
- Let \( A=\{x :|x^{2}-10|\le6\} \) and \( B=\{x :|x-2|>1\}. \) ThenJEE Mains 2026 Hard
- If the arithmetic mean and geometric mean of the \(p ^{\text {th }}\) and \(q ^{\text {th }}\) terms of the sequence \(-16,8,-4,2, \ldots\) satisfy the equation \(4 x^{2}-9 x+5=0,\) then \(p+q\) is equal to ..... .JEE Mains 2021 Hard
- The number of 4-letter words, with or without meaning, which can be formed using the letters of 'PQRPQRSTUVP', is:JEE Mains 2026 Hard
- Let \(f\) be a function such that \(f(x)+3 f\left(\frac{24}{x}\right)\) \(=4 x, x \neq 0\). Then \(f(3)+f(8)\) is equal toJEE Mains 2025 Easy
- If \(m\) is the \(A.M\) of two distinct real numbers \( l\) and \(n (l,n>1) \) and \(G_1, G_2\) and \(G_3\) are three geometric means between \(l\) and \(n\) then \(G_1^4 + 2G_2^4 + G_3^4\) equals :JEE Mains 2015 Hard
- If \(f(x)\, = sin\, (sin\,x)\) and \(f"(x) + tan\,xf'(x) + g(x)\, = 0\), then \(g(x)\) isJEE Mains 2013 Hard