MHT CET · Maths · Application of Derivatives
The approximate value of \(f(x)=3 x^{2}+5 x+3\) at \(x=3 \cdot 02\) is
- A \(45.46\)
- B \(v=45 \cdot 46\)
- C \(44 \cdot 76\)
- D \(44 \cdot 46\)
Answer & Solution
Correct Answer
(B) \(v=45 \cdot 46\)
Step-by-step Solution
Detailed explanation
Given \(f(x)=3 x^{2}+5 x+3 \Rightarrow f^{\prime}(x)=6 x+5\)
Let \(\mathrm{a}=3, \mathrm{~h}=0.02\)
\(\therefore \mathrm{f}(\mathrm{a}) \quad=\mathrm{f}(3)=27+15+3=45\)
\(f^{\prime}(a)=f^{\prime}(3) \quad=18+5=23\)
We know that
\(
\begin{aligned}
\mathrm{f}(\mathrm{a}+\mathrm{h}) & \div \mathrm{f}(\mathrm{a})+\mathrm{hf}^{\prime}(\mathrm{a})\end{aligned}\)
\(=45+(0.02)(23)=45+0.46=45.46\)
Let \(\mathrm{a}=3, \mathrm{~h}=0.02\)
\(\therefore \mathrm{f}(\mathrm{a}) \quad=\mathrm{f}(3)=27+15+3=45\)
\(f^{\prime}(a)=f^{\prime}(3) \quad=18+5=23\)
We know that
\(
\begin{aligned}
\mathrm{f}(\mathrm{a}+\mathrm{h}) & \div \mathrm{f}(\mathrm{a})+\mathrm{hf}^{\prime}(\mathrm{a})\end{aligned}\)
\(=45+(0.02)(23)=45+0.46=45.46\)
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 planes and pass through a straight line thenMHT CET 2018 Hard
- If \(f(x)=\frac{2 x+3}{3 x-2}, x \neq \frac{2}{3}\), then the function fof isMHT CET 2020 Easy
- If \(2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \operatorname{cosec} x)\), then the value of \(x\) isMHT CET 2021 Medium
- The equation of common tangent to the circle \(x^{2}+y^{2}=2\) and the parabola \(y^{2}=8 x\) is \(x+y-k\). Then value of \(k\) isMHT CET 2010 Medium
- Let ABCD be a quadrilateral with \(\overline{\mathrm{AB}}=\bar{a}, \overline{\mathrm{AD}}=\overline{\mathrm{b}}\) and \(\overline{\mathrm{AC}}=3 \bar{a}+2 \overline{\mathrm{~b}}\). If its area is \(\alpha\) times the area of the parallelogram with \(\mathrm{AB}, \mathrm{AD}\) as adjacent sides, then the value of \(\alpha\) is equal toMHT CET 2025 Medium
- The co-ordinates of foci of the ellipse \(16 x^{2}+9 y^{2}=144\) areMHT CET 2020 Easy
More PYQs from MHT CET
- The image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from \(25 / 3 \mathrm{~m}\) to \(50 / 7 \mathrm{~m}\) in 30 second. The speed of the object in \(\mathrm{km} / \mathrm{hr}\) isMHT CET 2025 Hard
- Fertilization of gametocytes of Plasmodium vivax takes place in ____________ .MHT CET 2022 Hard
- The instantaneous value of current in an a.c. circuit is \(I=3 \sin\) \(\left(50 \pi t+\frac{\pi}{4}\right) \mathrm{A}\). The current will be maximum for the first time atMHT CET 2025 Easy
- A particle executes linear S.H.M. with amplitude 4 cm . The magnitude of velocity and acceleration is equal when it is at 3 cm from mean position. Time period of oscillation isMHT CET 2025 Medium
- Semi-dwarf rice varieties were developed from _________ in Philippines.MHT CET 2020 Hard
- If \(x=-2+\sqrt{-3}\), then the value of \(2 x^4+5 x^3+7 x^2-x+38\) is equal toMHT CET 2025 Hard