TS EAMCET · Maths · Application of Derivatives
If \(m\) and \(M\) respectively denote the minimum and maximum of \(f(x)=(x-1)^2+3\) for \(x \in[-3,1]\), then the ordered pair \((m, M)\) is equal to
- A \((-3,19)\)
- B \((3,19)\)
- C \((-19,3)\)
- D \((-19,-3)\)
Answer & Solution
Correct Answer
(B) \((3,19)\)
Step-by-step Solution
Detailed explanation
Given that, \[ f(x)=(x-1)^2+3, \quad x \in[-3,1] \] On differentiating w.r.t. \(x\), we get \[ f^{\prime}(x)=2(x-1) \] For maxima and minima, put \(f^{\prime}(x)=0\) \[ \begin{aligned} \Rightarrow & & 2(x-1) & =0 \\ \Rightarrow & & x & =1 \end{aligned} \] Now,…
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
- Observe the following statements : \(\mathrm{A}: \int\left(\frac{x^2-1}{x^2}\right) e^{\frac{x^2+1}{x}} d x=e^{\frac{x^2+1}{x}}+c\) \(\mathrm{R}: \int f^{\prime}(x) e^{f(x)} d x=f(x)+c\) Then which of the following is true ?TS EAMCET 2006 Hard
- TS EAMCET 2021 Easy
- If the range of the real valued function \(f(x)=\frac{x^2+x+k}{x^2-x+k}\) is \(\left[\frac{1}{3}, 3\right]\), then \(k=\)TS EAMCET 2025 Medium
- The angles of a triangle are in the ratio \(3: 5: 10\). Then the ratio of the smallest side to the greatest side is :TS EAMCET 2006 Medium
- In \(\triangle A B C\), if \(a^2-c^2=b(b-c), \sqrt{2} a=2 b-c\) and \(R=\frac{1}{\sqrt{3}}\) then \(b=\)TS EAMCET 2020 Medium
- If \(\left|Z_1-3-4 i\right|=5\) and \(\left|Z_2\right|=15\) then the sum of the maximum and minimum values of \(\left|Z_1-Z_2\right|\) isTS EAMCET 2025 Hard
More PYQs from TS EAMCET
- \(\mathrm{AU}^{235}\) nuclear reactor generates energy at a rate of \(3.70 \times 10^7 \mathrm{~J} / \mathrm{s}\). Each fission liberates \(185 \mathrm{MeV}\) useful energy. If the reactor has to operate for \(144 \times 10^4 \mathrm{~s}\), then, the mass of the fuel needed is (Assume Avogadro's number \(\left.=6 \times 10^{23} \mathrm{~mol}^{-1}, 1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}\right)\)TS EAMCET 2013 Medium
- The order and degree of the differential equation \(\frac{d^2 y}{d x^2}+y+\left(\frac{d y}{d x}-\frac{d^3 y}{d x^3}\right)^{3 / 2}=0\), are respectively.TS EAMCET 2020 Easy
- Assertion \(\int_{-a}^a f(x) d x=\int_0^a(f(x)+f(-x)) d x\) Reason (R) \(\int_a^b f(x) d x=\int_{g(a)}^{g(b)} f(g(u)) g^{\prime}(u) d u\) The correct option among the following isTS EAMCET 2020 Easy
- If \(\frac{1}{\sin 45^{\circ} \sin 46^{\circ}}+\frac{1}{\sin 46^{\circ} \sin 47^{\circ}}+\ldots\) upto 45 terms \(=\frac{1}{\sin x^{\circ}}\), then \(\sin \left(\frac{\pi}{2} x\right)=\)TS EAMCET 2022 Hard
- In a photo electric experiment, the wavelength of the light incident on the metal is changed from \(200 \mathrm{~nm}\) to \(400 \mathrm{~nm}\). The decrease in the stopping potential is close to [Use \(\mathrm{hc}=1240 \mathrm{eV}-\mathrm{nm}\) where \(\mathrm{h}=\) Planck's constant and \(\mathrm{c}\) is velocity of light]TS EAMCET 2022 Medium
- The angle between the curves \(y^2=4 x+4\) and \(y^2=36(9-x)\) isTS EAMCET 2008 Medium