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Recent questions tagged maxima-minima

1 votes
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91
maxima , minima
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2 votes
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92
Maxima and minima
Could we always say that in case of local minima or maxima we do not consider the extreme points we only check for critical points while in case of absolute maxima we check both at end points as well as at critical point...Please correct me if I am wrong.
Could we always say that in case of local minima or maxima we do not consider the extreme points we only check for critical points while in case of absolute maxima we che...
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1 votes
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93
maxima minima problem
The greatest value of the function f(x) = 2 sin x + sin 2x on the interval [ 0,3pi/2 ] is ____ .
The greatest value of the function f(x) = 2 sin x + sin 2x on the interval [ 0,3pi/2 ] is ____ .
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0 votes
1 answer
94
Calculus maxima minima
True / false ? In continuous function if we have three stationary points then always it will be case that either one is maxima and two are minima or one is minima and two are maxima ? I think it is true but i am concerned about constant fucntion
True / false ?In continuous function if we have three stationary points then always it will be case that either one is maxima and two are minima orone is minima and two a...
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9 votes
2 answers
95
ISI2004-MIII: 12
The maximum possible value of $xy^2z^3$ subjected to condition $x,y,z \geq 0$ and $x+y+z=3$ is $1$ $\frac{9}{8}$ $\frac{9}{4}$ $\frac{27}{16}$
The maximum possible value of $xy^2z^3$ subjected to condition $x,y,z \geq 0$ and $x+y+z=3$ is$1$$\frac{9}{8}$$\frac{9}{4}$$\frac{27}{16}$
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5 votes
2 answers
96
ISI2004-MIII: 7
The equation $x^{6}-5x^{4}+16x^{2}-72x+9=0$ has exactly two distinct real roots exactly three distinct real roots exactly four distinct real roots six different real roots
The equation $x^{6}-5x^{4}+16x^{2}-72x+9=0$ hasexactly two distinct real rootsexactly three distinct real rootsexactly four distinct real rootssix different real roots
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35 votes
4 answers
97
GATE CSE 2017 Set 2 | Question: GA-9
The number of roots of $e^{x}+0.5x^{2}-2=0$ in the range $[-5,5]$ is $0$ $1$ $2$ $3$
The number of roots of $e^{x}+0.5x^{2}-2=0$ in the range $[-5,5]$ is$0$$1$$2$$3$
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35 votes
4 answers
98
GATE CSE 2017 Set 1 | Question: GA-8
The expression $\large \frac{(x+y) - |x-y|}{2}$ is equal to : The maximum of $x$ and $y$ The minimum of $x$ and $y$ $1$ None of the above
The expression $\large \frac{(x+y) - |x-y|}{2}$ is equal to :The maximum of $x$ and $y$The minimum of $x$ and $y$$1$None of the above
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6 votes
1 answer
102
ISRO2009-50
The value of $x$ at which $y$ is minimum for $y=x^2 -3x +1 $ is $-3/2$ $3/2$ $0$ $-5/4$
The value of $x$ at which $y$ is minimum for $y=x^2 -3x +1 $ is$-3/2$$3/2$$0$$-5/4$
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5 votes
3 answers
103
ISRO-2013-49
What is the least value of the function $f(x) = 2x^{2}-8x-3$ in the interval $[0, 5]$? $-15$ $7$ $-11$ $-3$
What is the least value of the function $f(x) = 2x^{2}-8x-3$ in the interval $[0, 5]$?$-15$$7$$-11$$-3$
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2 votes
2 answers
106
Solve
At $t=0$, the function $f(t)=\frac{\sin t}{t}$ has (A) a minimum (B) a discontinuity (C) a point of inflection (D) a maximum
At $t=0$, the function $f(t)=\frac{\sin t}{t}$ has(A) a minimum(B) a discontinuity (C) a point of inflection(D) a maximum
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0 votes
1 answer
107
maxima-minima query
consider the following function f(x) = x3 /3+ x2 /2 -6x+1000 find the intervals on which f is increasing. Is my solution right approach for this kind of numerical?? Caption
consider the following function f(x) = x3 /3+ x2 /2 -6x+1000find the intervals on which f is increasing.Is my solution right approach for this kind of numerical?? Caption...
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1 votes
2 answers
109
Find absolute minimum
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9 votes
6 answers
111
TIFR CSE 2014 | Part A | Question: 9
Solve min $x^{2}+y^{2}$ subject to $\begin {align*} x + y &\geq 10,\\ 2x + 3y &\geq 20,\\ x &\geq 4,\\ y &\geq 4. \end{align*}$ $32$ $50$ $52$ $100$ None of the above
Solve min $x^{2}+y^{2}$ subject to$$\begin {align*} x + y &\geq 10,\\2x + 3y &\geq 20,\\x &\geq 4,\\y &\geq 4.\end{align*}$$$32$$50$$52$$100$None of the above
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8 votes
2 answers
112
TIFR CSE 2013 | Part A | Question: 16
The minimum of the function $f(x) = x \log_{e}(x)$ over the interval $[\frac{1}{2}, \infty )$ is $0$ $-e$ $\frac{-\log_{e}(2)}{2}$ $\frac{-1}{e}$ None of the above
The minimum of the function $f(x) = x \log_{e}(x)$ over the interval $[\frac{1}{2}, \infty )$ is$0$$-e$$\frac{-\log_{e}(2)}{2}$$\frac{-1}{e}$None of the above
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10 votes
2 answers
114
TIFR CSE 2011 | Part A | Question: 4
Consider the problem of maximizing $x^{2}-2x+5$ such that $0< x< 2$. The value of $x$ at which the maximum is achieved is: $0.5$ $1$ $1.5$ $1.75$ None of the above
Consider the problem of maximizing $x^{2}-2x+5$ such that $0< x< 2$. The value of $x$ at which the maximum is achieved is:$0.5$$1$$1.5$$1.75$None of the above
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3 votes
1 answer
115
TIFR2010-Maths-A-6
The maximum value of $f(x)=x^{n}(1 - x)^{n}$ for a natural numbers $n\geq 1$ and $0\leq x\leq 1$ is $\frac{1}{2^{n}}$ $\frac{1}{3^{n}}$ $\frac{1}{5^{n}}$ $\frac{1}{4^{n}}$
The maximum value of $f(x)=x^{n}(1 - x)^{n}$ for a natural numbers $n\geq 1$ and $0\leq x\leq 1$ is$\frac{1}{2^{n}}$$\frac{1}{3^{n}}$$\frac{1}{5^{n}}$$\frac{1}{4^{n}}$
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7 votes
3 answers
116
TIFR CSE 2010 | Part A | Question: 3
The function $f (x) = 2.5 \log_e \left( 2 + \exp \left( x^2 - 4x + 5 \right)\right)$ attains a minimum at $x = $? $0$ $1$ $2$ $3$ $4$
The function $f (x) = 2.5 \log_e \left( 2 + \exp \left( x^2 - 4x + 5 \right)\right)$ attains a minimum at $x = $?$0$$1$$2$$3$$4$
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32 votes
4 answers
117
GATE CSE 2015 Set 2 | Question: GA-3
Consider a function $f(x) = 1- |x| \text{ on } -1 \leq x \leq 1$. The value of $x$ at which the function attains a maximum, and the maximum value of the function are: $0, -1$ $-1, 0$ $0, 1$ $-1, 2$
Consider a function $f(x) = 1- |x| \text{ on } -1 \leq x \leq 1$. The value of $x$ at which the function attains a maximum, and the maximum value of the function are:$0, ...
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22 votes
5 answers
118
GATE IT 2008 | Question: 31
If $f(x)$ is defined as follows, what is the minimum value of $f(x)$ for $x \in (0, 2]$ ? $f(x) = \begin{cases} \frac{25}{8x} &\text{ when } x \leq \frac{3}{2} \\ x+ \frac{1}{x} &\text { otherwise}\end{cases}$ $2$ $2 \frac{1}{12}$ $2\frac{1}{6}$ $2\frac{1}{2}$
If $f(x)$ is defined as follows, what is the minimum value of $f(x)$ for $x \in (0, 2]$ ?$$f(x) = \begin{cases} \frac{25}{8x} &\text{ when } x \leq \frac{3}{2} \\ x+ \fr...
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13 votes
1 answer
119
GATE CSE 1995 | Question: 25a
Find the minimum value of $3-4x+2x^2$.
Find the minimum value of $3-4x+2x^2$.
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26 votes
3 answers
120
GATE CSE 1995 | Question: 1.21
In the interval $[0, \pi]$ the equation $x=\cos x$ has No solution Exactly one solution Exactly two solutions An infinite number of solutions
In the interval $[0, \pi]$ the equation $x=\cos x$ has No solutionExactly one solutionExactly two solutionsAn infinite number of solutions
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