`L e tf(x)={(|x^3+x^2+3x+sinx|(3+sin(1/x)) ,, x!=0), (0 ,, x=0):}` then the number of point where `f(x)` attains its minimum value is_____

Write the point where f(x)=x\ (log)_e x attains minimum value.

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.

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.

If f(x)=(2x+3sinx)/(3x+2sinx) , x!=0 is continuous at x=0 , then find f(0)

Let f(x)={(e^x-1+ax)/x^2, x>0 and b, x=0 and sin(x/2)/x , x<0 , then

The function f(x)=((3^x-1)^2)/(sinx*ln(1+x)), x != 0, is continuous at x=0, Then the value of f(0) is

Let f(x)={(x(e^([x]+x)-4)/([x]+|x|), , x!=0),(3, , x=0):} Where [ ] denotes the greatest integer function. Then,

If f(x) ={:{((sin 3x)/(sin 5x)", "x ne 0),(0", " x= 0):}, then discuss its continuity at x= 0. .

f(x)=|a x-b|+c|x|AAx in (-oo,oo), where a >0, b >0,c > 0. Find the condition if f(x) attains the minimum value only at one point.

f(x)=|a x-b|+c|x|AAx in (-oo,oo), where a >0, b >0,c > 0. Find the condition if f(x) attains the minimum value only at one point.