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Maxima and Minima MATHS - Maxima and Minima

Rajasthan Board (RBSE) - STD 12 Science - MATHS (Rajasthan - English Medium). 138 questions in this chapter.

Question types

Maxima and Minima question types

138 questions across 4 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

138
Questions
4
Question groups
5
Question types
Sample Questions

Maxima and Minima questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
If $\text{f}(\text{x})=\frac{1}{4\text{x}^{2}+2\text{x}+1}$, then its maximum value is :
  • ✓
    $\frac{4}{3}$
  • B
    $\frac{2}{3}$
  • C
    $1$
  • D
    $\frac{3}{4}$

Answer: A.

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Q 2M.C.Q (1 Marks)1 Mark
If a cone of maximum volume is inscribed in a given sphere, then the ratio of the height of the cone to the diameter of the sphere is :
  • A
    $\frac{3}{4}$
  • B
    $\frac{1}{3}$
  • C
    $\frac{1}{4}$
  • ✓
    $\frac{2}{3}$

Answer: D.

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Q 3M.C.Q (1 Marks)1 Mark
The sum of two non-zero number is 8, the minimum value of the sum of the reciprohcle is :
  • A
    $\frac{1}{4}$
  • ✓
    $\frac{1}{2}$
  • C
    $\frac{1}{8}$
  • D
    None of these.

Answer: B.

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Q 123 Marks Question3 Marks
Find the points o local maxima or local minima, if any, of the following functions, using the first derivatives test. Also, find the local maximum or local minimum values, as the case may be:
$\text{f}(\text{x})=\text{x}\sqrt{1-\text{x}}, \text{x}\geq0$
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Q 133 Marks Question3 Marks
Find the points o local maxima or local minima, if any, of the following functions, using the first derivatives test. Also, find the local maximum or local minimum values, as the case may be:
$\text{f}(\text{x})=\text{x}^{3}-6\text{x}^{2}+9\text{x}+15$
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Q 143 Marks Question3 Marks
Manufacturer can sell x items at a price of rupees $(5-\frac{\text{x}}{100})$ each. The cost price is Rs $\Big(\frac{\text{x}}{5}+500\Big)$. Find the number of items he should sell to earn maximum profit.
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Q 153 Marks Question3 Marks
Find the points o local maxima or local minima, if any, of the following functions, using the first derivatives test. Also, find the local maximum or local minimum values, as the case may be:
$f(x) = (x - 5)^4$
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Q 165 Marks Questions5 Marks
A wire of length 28m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the lengths of the two pieces so that the combined area of the circle and the square is minimum?
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Q 175 Marks Questions5 Marks
Find the points of local maxima or local minima and corresponding local maximum and local minimum values of the following functions. Also, find the points of inflection,
$\text{f}(\text{x})=\text{x}+\sqrt{1-\text{x}},\text{x}\leq 1$
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Q 185 Marks Questions5 Marks
A beam is supported at the two ends and is uniformly loaded. The bending moment M at a distance x from one end is given by
$\text{M}=\frac{\text{WL}}{2}\text{x}-\frac{\text{W}}{2}\text{x}^{2}$
Find the point at which M is maximum in each case.
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Q 195 Marks Questions5 Marks
Find the points of local maxima or local minima and corresponding local maximum and local minimum values of the following functions. Also, find the points of inflection,
$f(x) = (x - 1)(x - 2)^2$
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Q 205 Marks Questions5 Marks
A tank with rectangular base and rectangular sides, open at the top is to the constructed so that its depth is 2m and volume is $8m^3$. If building of tank cost 70 per square metre for the base and Rs 45 per square matre for sides, what is the cost of least expensive tank?
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