`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.

If the fucntion f(x)={{:(asqrt(x+7),,,0lexlt2),(bx+5,,,x ge2):} is differentiable AA x ge0 , then 2a+4b is equal to

If the function f(x)={{:(asqrt(x+7),":",0lexlt9),(bx+5,":",xge9):} is differentiable for xge0 , then the value of 5a+6b is equal to

If f(x)={x^2+3x+a ,xlt=1, b x+2, forx >1 is everywhere differentiable, find the values of aa n dbdot

Let f(x)={((alpha cotx)/x+beta/x^2 ,, 0<|x|lt=1),(1/3 ,, x=0):} . If f(x) is continuous at x=0 then the value of alpha^2+beta^2 is

Let f (x)= {{:(a-3x,,, -2 le x lt 0),( 4x+-3,,, 0 le x lt 1):},if f (x) has smallest valueat x=0, then range of a, is

Let f(x)={{:(1+(2x)/(a)", "0lexlt1),(ax", "1lexlt2):}."If" lim_(xto1) "f(x) exists, then a is "

Show that the function f(x)={:{(3+x", " xge0),(3-x", " x lt 0):} is not differentiable at x=0

Let f (x)= {{:(x ^(2),0lt x lt2),(2x-3, 2 le x lt3),(x+2, x ge3):} then the tuue equations:

Let f(x)={{:(1+x",", 0 le x le 2),(3-x"," ,2 lt x le 3):} find (fof) (x).

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 .