TS EAMCET · Maths · Application of Derivatives
A real valued function \(f(x)=\left|x^2-3 x+2\right|+2 x-3\) is defined on \([-2,1]\). If m and M are absolute minimum and absolute maximum values of \(f\) respectively then \(\mathrm{M}-4 \mathrm{~m}=\)
- A \(0\)
- B \(1\)
- C \(15\)
- D \(10\)
Answer & Solution
Correct Answer
(D) \(10\)
Step-by-step Solution
Detailed explanation
\(f(x)=\left|x^2-3 x+2\right|+2 x-3\) For \(x \in [-2,1]\), \(x^2-3x+2=(x-1)(x-2) \ge 0\). \(f(x)=x^2-3x+2+2x-3 = x^2-x-1\) To find extremum, find derivative: \(f'(x)=2x-1\) Set \(f'(x)=0 \Rightarrow 2x-1=0 \Rightarrow x=1/2\). Evaluate \(f(x)\) at \(x=-2, 1/2, 1\):…
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 the tangent and normal drawn to the curve \(x=a(\theta+\sin \theta), y=a(1-\cos \theta)\) at \(P\left(\theta=\frac{\pi}{2}\right)\) cuts the \(\mathrm{X}\)-axis at \(A\) and \(B\) respectively, then the area (in sq. units) of \(\triangle P A B\) isTS EAMCET 2020 Medium
- The number of natural numbers less than 1000 in which no digit is repeated isTS EAMCET 2018 Medium
- If the image of the point \((1,-2,1)\) with respect to the line passing through the points \(\mathrm{B}(1,1,2)\) and \(\mathrm{C}(2,2,1)\) is \((1, m, n)\), then \(1^2+m^2+n^2=\) (a) 1 (b) 9 (c) 22 (d) 26TS EAMCET 2023 Easy
- If \(f: N \rightarrow Z\) is defined by \[ f(n)=\left\{\begin{array}{l} 2 \text { if } n=3 k, k \in Z \ 10 \text { if } n=3 k+1, k \in Z \ 0 \text { if } n=3 k+2, k \in Z \end{array}\right. \] Then , \(\{n \in N: f(n)>2\}\) is equal toTS EAMCET 2004 Easy
- The point if intersection of the lines \(l_1: \mathbf{r}(t)=(\mathbf{i}-6 \mathbf{j}+2 \mathbf{k})+t(\mathbf{i}+2 \mathbf{j}+\mathbf{k})\) \(l_2: \mathbf{R}(u)=(4 \mathbf{j}+\mathbf{k})+u(2 \mathbf{i}+\mathbf{j}+2 \mathbf{k})\) isTS EAMCET 2012 Medium
- \(\frac{1}{e^{3 x}}\left(e^x+e^{5 x}\right)=a_0+a_1 x+a_2 x^2+\ldots\) \(\Rightarrow \quad 2 a_1+2^3 a_3+2^5 a_5+\ldots\) is equal toTS EAMCET 2009 Medium
More PYQs from TS EAMCET
- Given the fact that
A) Magnetic field exerts force only on a moving charge
B) Electric field exerts force on both stationary and moving charge
C) Magnetic field exerts force on charge moving parallel to the direction of the field.
Which of the following is true?TS EAMCET 2021 Medium - If \(\quad \cos 2 x=(\sqrt{2}+1)\left(\cos x-\frac{1}{\sqrt{2}}\right), \cos x \neq \frac{1}{2}\), then \(x \in\)TS EAMCET 2005 Hard
- From the following energy levels of hydrogen atom, the values of \(E_{\infty}\) and \(E_3\) in \(\mathrm{J}\) are, respectively \[ \begin{aligned} -E_{\infty} & =\ldots \ldots \ldots \ -E_3 & =\ldots \ldots \ldots \ -E_2 & =-0.545 \times 10^{-18} \mathrm{~J} \ - & E_1=-2.18 \times 10^{-18} \mathrm{~J} \end{aligned} \]TS EAMCET 2019 Medium
- The solutions of the equation \(z^2\left(1-z^2\right)=16\), \(z \in \mathbf{C}\), lie on the curveTS EAMCET 2020 Medium
- If the curves \(a x^2+b y^2=1\) and \(c x^2+d y^2=1\) intersect orthogonally, then \(\frac{b-a}{d-c}=\)TS EAMCET 2020 Medium
- Let \(A=\{x \in R, x \neq 0,-4 \leq x \leq 4\} \quad\) and \(f: A \rightarrow R\) defined by \(f(x)=\frac{|x|}{x}\) for \(x \in A\). Then, the range of \(f\) isTS EAMCET 2002 Easy