if `f(x)={(x^2,xle1),(ax+b,x>1):}` is differentiable at x = 1, find the values of a and b. Hence find f'(1)

f(x)={(x^2+2x, "" xle0,),(ax+b, "" x >0,):} is continuous and differentiable at x =0, find the values of a and b

if f (x) = x^4-62x^2+ax+9 attains its local maximum value at x= 1, find the value of a

Examine differentiability at x= 1 and x=0 f(x)={(-x, x 1, ):}

If f(x) = 2^x then find the value of Delta2^x , for x= 2 and h= 1.

Find the domain and range of f if . f(x)=1/(x^2-1)

Find the domain and range of f if . f(x)=sqrt(1-x)

Find the domain and range of f if . f(x)=1/(x(x-1))