WBJEE · Maths · Application of Derivatives
Let \(f(x)\) be a differentiable function in \([2,7]\). If \(f(2)=3\) and \(f^{\prime}(x) \leq 5\) for all \(x\) in \((2,7),\) then the maximum posaible value of \(f(x)\) at \(x=7\) is
- A 7
- B 15
- C 28
- D 14
Answer & Solution
Correct Answer
(C) 28
Step-by-step Solution
Detailed explanation
Given, \(\quad f^{\prime}(x) \leq 5\) \(\frac{f(7)-f(2)}{x-2} \leq 5\) (by Lagrange mean value theorem] \(\begin{array}{ll}\Rightarrow & \frac{f(7)-3}{7-2} \leq 5 \\ \Rightarrow & f(7) \leq 5(7-2)+3 \\ \therefore & f(7) \leq 28\end{array}\)
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 for a matrix \(A,|A|=6\) and adj \(A=\left[\begin{array}{ccc}1 & -2, & 4 \\ 4 & 1 & 1 \\ -1 & k & 0\end{array}\right]\), then \(k\) is equal toWBJEE 2025 Medium
- The displacement \(\mathrm{x}\) of a particle at time \(\mathrm{t}\) is given by \(\mathrm{x}=\mathrm{At}^2+\mathrm{Bt}+\mathrm{C}\) where \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) are constants and \(\mathrm{v}\) is velocity of a particle, then the value of \(4 \mathrm{Ax}-\mathrm{v}^2\) isWBJEE 2010 Easy
- If \(I=\int \frac{x^2 d x}{(x \sin x+\cos x)^2}=f(x)+\tan x+c\), then \(f(x)\) isWBJEE 2023 Medium
- A family of curves is such that the length intercepted on the \(y\) -axis between the origin and the tangent at a point is three times the ordinate of the point of contact. The family of curves isWBJEE 2013 Medium
- Let \(f\) and \(g\) be differentiable on the interval \(I\) and let \(a, b \in I, a < b\). Then,WBJEE 2019 Medium
- The minimum value of \(2^{\sin x}+2^{\cos x}\) isWBJEE 2014 Medium
More PYQs from WBJEE
- Four resistors, \(100 \Omega, 200 \Omega, 300 \Omega\) and \(400 \Omega\) are connected to form four sides of a square. The resistors can be connected in any order. What is the maximum possible equivalent resistance across the diagonal of the square?WBJEE 2018 Medium
- The value of \(\lim _{x \rightarrow 0} \frac{\int_{0}^{x^{2}} \cos \left(t^{2}\right) d t}{x \sin x}\) isWBJEE 2014 Easy
- The eccentric angle in the first quadrant of a point on the ellipse \(\frac{x^{2}}{10}+\frac{y^{2}}{8}=1\) at a distance 3 units from the centre of the ellipse isWBJEE 2012 Easy
- Let \(\left(1+x+x^{2}\right)^{9}=a_{0}+a_{1} x+a_{2} x^{2}\)
\(+\ldots+a_{18} x^{18} \cdot\) ThenWBJEE 2017 Medium - The correct order of boiling point of the given aqueous solution isWBJEE 2024 Medium
- The value of the expression \({ }^{47} \mathrm{C}_4+\sum_{\mathrm{j}=1}^5{ }^{52-\mathrm{j}} \mathrm{C}_3\) isWBJEE 2025 Medium