Show that `f(x)={12 x-13 ,\ \ \ if\ xlt=3 2x^2+5,\ \ \ \ \ if\ x >3` is differentiable at `x=3` . Also, find `f^(prime)(3)` .

Show that f(x)={12 x-13 , ifxlt=3 , 2x^2+5 ifx >3 is differentiable at x=3 . Also, find f^(prime)(3)dot

Show that f(x)={12 x-13 ,2x^2+5, ifxlt=3ifx >3 is differentiable at x=3 . Also, find f^(prime)(3)dot

Show that f(x)={12x-13,quad if quad x is differentiable at x=3. Also,find f'(3)

Show that f (x) = 2x +3 is differentiable at x=1 and hence find f'(1).

If f(x)={a x+b ,\ xlt=-1a x^3+x+2,\ x > -1 is differentiable for all x in R\ fin d\ \ ^(prime)a^(prime)&\ ' b '

If f(x)={x^2+3x+a ,\ \ \ for\ xlt=1b x+2,\ \ \ \ \ \ \ \ \ \ \ \ \ for\ x >1 is everywhere differentiable, find the values of a and b .

Show that the function f(x)=x^3/2 is not differentiable at x=0.

Show that the function f(x)=x^(3/2) is not differentiable at x=0.

Let f(x) =[{:(asqrt(x+1),0lt xlt3),(bx +2, 3lexlt5):} if f(x) is differentiable at x=3 then find the values of a and b.

Show that the function f (x) = {{:( x, if x lt 1), ( 6 -2x , if 1 le x le 3), ( x ^(2) - 4x + 3, if x gt 3):} is not differentiable at x = 1,3