AP EAMCET · Maths · Application of Derivatives
The absolute minimum value of \(x^4-x^2-2 x+5\) is
- A equal to 5
- B equal to 3
- C equal to 7
- D Does not exist
Answer & Solution
Correct Answer
(B) equal to 3
Step-by-step Solution
Detailed explanation
\(x^4-x^2-2 x+5=f(x)\) (say) Then, \(f^{\prime}(x)=4 x^3-2 x-2\) Equate \(f^{\prime}(x)=0 \Rightarrow 4 x^3-2 x-2=0\) \(\Rightarrow \quad 2 x^3-x-1=0\) \(\Rightarrow \quad 2 x\left(x^2-1\right)+(x-1)=0\) \(\Rightarrow \quad 2 x(x-1)(x+1)+(x-1)=0\)…
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 \(\int \frac{d x}{x(\log x-2)(\log x-3)}=I+C\), then \(I\) is equal toAP EAMCET 2013 Hard
- Let \(a\gt1\) and \(0 \lt b \lt 1\). If \(f: \mathbf{R} \rightarrow[0,1]\) is defined by
\(f(x)=\left\{\begin{array}{l}a^x,-\infty \lt x \lt 0 \\ b^x, 0 \leq x \lt \infty\end{array}\right.\) then \(f(x)\) isAP EAMCET 2024 Medium - If a point \((a, a)\) falls between the lines \(|x+y|=4\), thenAP EAMCET 2021 Easy
- For \(x \in \mathbb{R}\), the minimum value of \(\frac{x^2+2 x+5}{x^2+4 x+10}\) isAP EAMCET 2023 Easy
- The order and degree of the differential equation \(\sqrt{\frac{d y}{d x}}-4 \frac{d y}{d x}-7 x=0\) are respectivelyAP EAMCET 2021 Easy
- If \(f(x)=\left\{\begin{array}{cc}2 x+3, & x \leq 1 \\ a x^2+b x, & x\gt1\end{array}\right.\) is differentiable \(\forall x \in \mathbb{R}\), then \(f(2)=\)AP EAMCET 2024 Easy
More PYQs from AP EAMCET
- If \(A=\left[\begin{array}{cc}i & 0 \\ 0 & -i\end{array}\right], B=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]\) and \(C=\left[\begin{array}{ll}0 & i \\ i & 0\end{array}\right]\), thenAP EAMCET 2023 Easy
- The number of solutions for \(z^3+\bar{z}=0\), isAP EAMCET 2014 Easy
- If \(\mathrm{A}\) and \(\mathrm{B}\) are two events of a random experiment such that \(P(A \cup B)=0.65\) and \(P(A \cap B)=0.15\), then \(\mathrm{P}(\overline{\mathrm{A}})+\mathrm{P}(\overline{\mathrm{B}})=\)AP EAMCET 2023 Easy
- \(\int \frac{1-x^7}{x\left(1+x^7\right)} d x=a \ln |x|+b \ln \left|x^7+1\right|+c \Rightarrow(a, b)=\)AP EAMCET 2017 Hard
- The differential equation formed by eliminating \(\mathrm{A}\) and \(\mathrm{B}\) from \(\mathrm{A} x^2+\mathrm{B} y^2=1\) isAP EAMCET 2017 Medium
- Three Carnot engines operate in series between a heat source at temperature \(T_1\) and heat sink at a temperature \(T_4\). There are two other reservoirs at temperatures \(T_2\) and \(T_3\). The three engines are equally efficient, if (given that, \(\left.T_1>T_2>T_3>T_4\right)\)
AP EAMCET 2021 Hard