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 ,xlt=1b x+2,forx >1 is everywhere differentiable, find the values of aa n dbdot

If f(x)={ax^(2)+b,x 1;b!=0, then f(x) is continuous and differentiable at x=1 if

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.

If f (x) = ae^(|x|)+b|x|^(2); a","b epsilon R and f(x) is differentiable at x=0.Then ,a and b are

If f(x)=|(log)_e|x| , then f(x) is continuous and differentiable for all x in its domain] (b) f(x) is continuous for all x in its domain but not differentiable at x=+-1 (c) f(x) is neither continuous nor differentiable at x=+-1 (d) none of these

If f(x)={{:(a+tan^(-1)(x-b),,,x ge1),((x)/(2),,,xlt1):} is differentiable at x = 1, then 4a-b can be

If f(x)=|ln|x|, then (a)f(x) is continuous and differentiable for all x in its domain (b) f(x) is continuous for all for all x in its domain but not differentiable at x=+-1 (c) f(x) is neither continuous nor differentiable at x=+-1 (d) none of these

Let f(x y)=f(x)f(y)\ AA\ x ,\ y in R and f is differentiable at x=1 such that f^(prime)(1)=1 also f(1)!=0 , f(2)=3 , then find f^(prime)(2) .

Let f(x)=[x e^x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ xlt=0x+x^2-x^3\ \ \ \ \ \ x >0 then prove that f is continuous and differentiable for all xdot f' is continuous and differentiable for all xdot

If f(x) =ax^(2) + bx + c satisfies the identity f(x+1) -f(x)= 8x+ 3 for all x in R Then (a,b)=