Let `f(x)={x^3-x^2+10 x-5,xlt=1-2x+(log)_2(b^2-2),x >1` Find the values of `b` for which `f(x)` has the greatest value at `x=1.`

Let f (x) = {{:( x^(3) - x^(2) + 10 x- 5 , "," , x le 1), ( -2x + log _(2) (b^(2) - 2) , "," , x gt 1):} the set of values of b for which f(x) has greatest value at x = 1 is given by

Let f(x)={-x^(3)+log2b,0 =1} Then minimum value of b-11 for which f(x) has least value at x=1 is

Let f(x)={(-x^(3)+log_(2)a,0<=x<1),(3x,1<=x<=3)} ,the complete set of real values of a for which f(x) has smallest value at x=1 is

If f(x)=x^(2+x+1 , then find the value of 'x' for which f(x-1) =f(x)

Let f(x)= (2x)/(2x^2+5x+2) and g(x)=1/(x+1) . Find the set of real values of x for which f(x) gt g(x) .

If 2f(x)+3f(-x)=x^(2)-x+1, find the value of f'(1)

If f (x) = x^(2) -2x + 3, then the value of x for which f (x) = f(x +1) is

If f(x)={x ,\ xlt=1x^2+b x+c ,\ x >1 , then find the values of b\ a n d\ c if f(x) differentiability at x=1.