Let f (x)= {{:(1+ sin x "," , x lt 0),( ...

Let `f (x)= {{:(1+ sin x "," , x lt 0),( x ^(2) -x+1",", x ge 0):},` then:

A

f has a local maximum at `x=0`

B

f has a local minimum at `x=0`

C

f is increasing everywhere

D

f is decreasing everywhere

Text Solution

Verified by Experts

The correct Answer is:

A

Topper's Solved these Questions

APPLICATION OF DERIVATIVES
VK JAISWAL ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ANSWER IS/ARE CORRECT )|29 Videos
APPLICATION OF DERIVATIVES
VK JAISWAL ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|15 Videos
AREA UNDER CURVES
VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|8 Videos

Similar Questions

Explore conceptually related problems

If f (x)= [{:( cos x ^(2),, x lt 0),( sin x ^(3) -|x ^(3)-1|,, x ge 0):} then find the number of points where f (x) =f )|x|) is non-difierentiable.

if f(x) ={{:( x-1, xlt 0),( x^(2) - 2x , x ge 0):} , then

In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0):} then find the number of points where g (x) =f (|x|) is non-differentiable.

Let f (x) = {{:(min (x"," x ^(2)), x ge 0),( max (2x "," x-1), x lt 0):}, then which of the following is not true ?

Discuss of the continutiy of the fuction f(x)={{:(sin x/x ", " x lt 0),(x+2 "," x ge 0):}

If f(x) = {{:(x - 3",",x lt 0),(x^(2)-3x + 2",",x ge 0):}"and let" g(x) = f(|x|) + |f(x)| . Discuss the differentiability of g(x).

Discuss the continutiy of the function f(x)= {((sin x)/x", " x lt 0),(2x+3 ", " x ge 0 ):}

Let f(x){:{(1+sinx", "xlt0),(x^(2)-x+1ge0):} Then

Let f (x)= {{:(2-x"," , -3 le x le 0),( x-2"," , 0 lt x lt 4):} Then f ^(-1) (x) is discontinous at x=

Let f(x)= {{:((x)/(1+|x|)",", |x| ge1), ((x)/(1-|x|)",", |x| lt 1):}, then domain of f'(x) is:

VK JAISWAL ENGLISH-APPLICATION OF DERIVATIVES -EXERCISE (SUBJECTIVE TYPE PROBLEMS)

Let f (x)= {{:(1+ sin x "," , x lt 0),( x ^(2) -x+1",", x ge 0):}, the...
Text Solution
|
A conical vessel is to be prepared out of a circular sheet of metal of...
Text Solution
|
On [1,e], then least and greatest vlaues of f (x) = x^(2)ln x are m a...
Text Solution
|
If f (x)= (px)/(e ^(x)) - (x ^(2))/(2) + x is a decreasing function f...
Text Solution
|
Let f (x)= {{:( xe ^(ax)"," , x le 0),( x+ ax ^(2)-x ^(3)"," , x gt 0)...
Text Solution
|
Find sum of all possible values of the real parameter 'b' if the diffe...
Text Solution
|
Let 'theta' be the angle in radians between the curves (x ^(2))/(36) +...
Text Solution
|
Let set of all possible values of lamda such that f (x)= e ^(2x) - (la...
Text Solution
|
Let a,b,c and d be non-negative real number such that a ^(5)+b^(5) le ...
Text Solution
|
There is a point (p,q) on the graph of f(x)=x^(2) and a point (r,s) on...
Text Solution
|
If f(x)=max| 2 siny-x|, (where y in R), then find the minimum value o...
Text Solution
|
Let f (x) = int (0)^(x) ((a -1) (t ^(2)+t+1)^(2) -(a+1)(t^(4)+t ^(2) +...
Text Solution
|
The numbr of real roots of the equation x ^(2013)+ e ^(20144x) =0 is
Text Solution
|
Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(...
Text Solution
|
The least positive vlaue of the parameter 'a' for which there exist at...
Text Solution
|
Let f (x) =x ^(2) +2x -t ^(2) and f(x)=0 has two root alpha (t ) and b...
Text Solution
|
A tank contains 100 litres of fresh water. S solution containg 1 gm/li...
Text Solution
|
If f (x) is continous and differentiable in [-3,9] and f'(x) in [-2,8]...
Text Solution
|
It is given that f (x) is defined on R satisfying f (1)=1 and for AA ...
Text Solution
|
The number of normals to the curve 3y ^(3) =4x which passes through th...
Text Solution
|
Find the number of real root (s) of the equation ae ^(x) =1+ x + (x ^(...
Text Solution
|