AP EAMCET · Maths · Application of Derivatives
The function \(f(x)=x^3+a x^2+b x+c, a^2 \leq 3 b\) has
- A one maximum value
- B no extreme value
- C one maximum and one minimum value
- D one maximum and one minimum value
Answer & Solution
Correct Answer
(C) one maximum and one minimum value
Step-by-step Solution
Detailed explanation
Given, \(f(x)=x^3+a x^2+b x+c, a^2 \leq 3 b\). On differentiating w.r.t. \(x\), we get \(\begin{aligned} & f^{\prime}(x)=3 x^2+2 a x+b \\ & \text { Put } \quad f^{\prime}(x)=0 \\ & \Rightarrow \quad 3 x^2+2 a x+b=0 \\ & \end{aligned}\)…
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
- The number of ways of selecting 3 numbers that are in G.P. from the set \(\{1,2,3, \ldots, 100\}\) isAP EAMCET 2024 Easy
- The area of the region (in sq. units) enclosed between the curves \(y=|x|, y=[x]\) and the ordinates \(x=-1, x=0, x=1\) isAP EAMCET 2025 Medium
- If the equation of the plane passing through the point and perpendicular to the vector is thenAP EAMCET 2022 Easy
- Find the value(s) of \(k\) such that the distance between the two parallel lines represented by \((x-2 y)^2+k(x-2 y)=0\) is 3 unitsAP EAMCET 2021 Medium
- The vertices of a triangle are at \(-\hat{i}+3 \hat{j}\) and \(2 \hat{i}+5 \hat{j}\) and its orthocenter is at \(\bar{i}+2 \bar{j}\). If the position vector of the third vertex is \(a \hat{i}+b \hat{j}\), then \((a, b)=\)AP EAMCET 2022 Easy
- \(\frac{1}{e^{3 x}}\left(e^x+e^{5 x}\right)=a_0+a_1 x+a_2 x^2+\ldots\)
\(\Rightarrow \quad 2 a_1+2^3 a_3+2^5 a_5+\ldots\) is equal toAP EAMCET 2009 Medium
More PYQs from AP EAMCET
- How many tripeptides can be prepared by linking the amino acids glycine, alanine and phenyl alanine?AP EAMCET 2009 Medium
- The values of \(\theta\), for which \(\frac{3+2 i \sin \theta}{1-2 i \sin \theta}\) is real areAP EAMCET 2022 Easy
- The point of concurrence of the polars of the variable point \((2 t, t-4), t \in \mathbb{R}\) with respect to the circle \(x^2+y^2-4 x-6 y+1=0\) isAP EAMCET 2017 Easy
- When sodium is dissolved in liquid ammonia, a deep blue coloured solution obtained. This colour of the solution is due toAP EAMCET 2020 Easy
- An aromatic compound "A" on treatment with \(\mathrm{Zn} / \mathrm{NH}_4 \mathrm{Cl}\) and subsequent heating with ammonical silver nitrate solution gives a black precipitate. Which functional groups does "A" contain?AP EAMCET 2020 Easy
- The anions (A) of \(\mathrm{C}_{\mathrm{p}} \mathrm{A}_{\mathrm{q}}\) molecule forms an fcc lattice. Cations (C) are positioned at the body center and half of the edge centers. The formula of the molecule isAP EAMCET 2022 Medium