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 evrywhere

D

f is decreasing everwhere

Verified by Experts

The correct Answer is:

A

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: