### Mathematics - Maxima And Minima

#### Question - 1

The points of extremum of the function $F(x)=\int _{ 1 }^{ x }{ { e }^{ -{ t }^{ 2 }/2 } } (1-{ t }^{ 2 })$ dt are

• A ±1
• B 0
• C ±1/2
• D ±2

#### Question - 2

A function f such that f' (2) = f" (2) = 0 and f has a local maximum of -17 at 2 is

• A (x-2)4
• B 3-(x-2)4
• C -17-(x-2)4
• D none of these

#### Question - 3

The difference between the greatest and the least value of the function $f\left( x \right) =\int _{ 0 }^{ x }{ \left( { t }^{ 2 }+t+1 \right) } dt$ on [2,3] is

• A 37/6
• B 47/6
• C 57/6
• D 59/6

#### Question - 4

Let f(x) = a -(x-3)8/9 then maxima of f(x) is

• A 3
• B a-3
• C a
• D none of these

#### Question - 5

Let f(x) be a differential function for all x, if f(1) = - 2 and f' (x) ≥2 for all x in [1, 6], then minimum value of f(6) is equal to

• A 2
• B 4
• C 6
• D 8

#### Question - 6

The point in the interval [0,2π], where f(x)=ex sin x has maximum slope is

• A $\frac { \pi }{ 4 }$
• B $\frac { \pi }{ 2 }$
• C $\pi$
• D none of these

#### Question - 7

Let $f(x)=\begin{cases} \left| { x }^{ 3 }+{ x }^{ 2 }+3x+sinx \right| \left( 3+sin\frac { 1 }{ x } \right) ,x\neq 0 \\ 0,\quad x=0 \end{cases}$then number of points (where f(x) attains its minimum value) is

• A 1
• B 2
• C 3
• D infinite many

#### Question - 8

If $f(x)={ alog }_{ e }\left| x \right| +{ bx }^{ 2 }+x$ has extremum at x = 1 and x = 3, then

• A a = - 3/4, b = -1/8
• B a = 3/4, b = -1/8
• C a = - 3/4, b = 1/8
• D none of these

#### Question - 9

Let f(x) = 1 + 2x2 + 22 x4 + .... + 210 x20 Then f(x) has

• A more than one minimum
• B exactly one minimum
• C at least one maximum
• D none of the above

#### Question - 10

Let $f(x)=\begin{cases} { sin }^{ -1 }\alpha +{ x }^{ 2 },\quad 0<x<1 \\ 2x,\quad x\ge 1 \end{cases}$f(x) can have a minimum at x = 1 is the value of ∝ is

• A 1
• B -1
• C 0
• D none of these