Maxima and Minima - Rajasthan Board (RBSE) STD 12 Science MATHS Questions

Q 1M.C.Q (1 Marks)1 Mark

The minimum value of $\frac{\text{x}}{\log_{\text{e}}\text{x}}$ is .

$\text{e}$
$\frac{1}{\text{e}}$
$1$
None of these

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Q 2M.C.Q (1 Marks)1 Mark

if $\text{ax}+\frac{\text{b}}{\text{x}}\geq\text{c}$ for all positive x where a, b, > 0, then.

$\text{ab} < \frac{\text{c}^{2}}{4}$
$\text{ab} > \frac{\text{c}^{2}}{4}$
$\text{ab} > \frac{\text{c}}{4}$
$\text{None of these}$

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Q 3M.C.Q (1 Marks)1 Mark

$\text{f}(\text{x})=\sin +\sqrt{3}\cos\text{x}$ is maximum when x =

$\frac{\pi}{3}$
$\frac{\pi}{4}$
$\frac{\pi}{6}$
$0$

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Q 4M.C.Q (1 Marks)1 Mark

The minimum value of $(\text{x}^{2}+\frac{250}{\text{x}})$ is:

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Q 5M.C.Q (1 Marks)1 Mark

The function $f(x) = 2x^3- 15x^2 + 36x + 4$ is maximum at $x =$

A
$3$
B
$0$
C
$4$
✓
$2$

Answer: D.

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Q 62 Marks Questions2 Marks

Write the minimum value of $\text{f}(\text{x})=\text{x}+\frac{1}{\text{x}},\text{x}>0.$

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Q 72 Marks Questions2 Marks

Write necessary condition for a point x = c to be an extreme point of the function f(x).

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Q 82 Marks Questions2 Marks

If f(x) attains a local minimum at x = c, then write the values of f' (c) and f'' (c).

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Q 92 Marks Questions2 Marks

Write sufficient condition for a point x = c to be an extreme point of the function f(x).

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Q 102 Marks Questions2 Marks

Write the point where $\text{f}(\text{x})=\text{x}\log_{\text{e}}\text{x}$ attains minimum value.

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Q 113 Marks Question3 Marks

Write the minimum value of $\text{f}(\text{x})=\text{x}+\frac{1}{\text{x}},\text{x}>0.$

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Q 123 Marks Question3 Marks

Show that $\frac{\text{logx}}{\text{x}}$ has a minimum value at x = e.

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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:
$\text{f}(\text{x})=\text{x}\sqrt{1-\text{x}}, \text{x}\geq0$

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Q 143 Marks Question3 Marks

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Q 153 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 165 Marks Questions5 Marks

Prove that the semi-vertical angle of the right circular cone of given volume and least curved surface is $\cos^{-1}(\sqrt{2})$ .

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Q 175 Marks Questions5 Marks

An isosceles triangle of vertical angle 2θ is inscribed in a circle of radius a. Show that the area of the triangle is maximum when $\theta = \frac{\pi}{6}.$

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Q 185 Marks Questions5 Marks

Find the maximum and minimum values of $\text{y}=\tan \text{x}-2\text{x}$

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Q 195 Marks Questions5 Marks

If $f(x) = x^3 + ax^2 + bx + c$ has a maximum at $x = -1$ and minimum at $x = 3.$ Determine $a, b$ and $c.$

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Q 205 Marks Questions5 Marks

Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is $6\sqrt{3}\text{ r}$.

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