If `f(x)={x ,xlt=1x^2+b x+c ,x >1'`

Consider the function f(x)={2x+3,xlt=1-x^2+6,x >1

Find the values of a and b , if the function f defined by f(x)={x^2+3x+a ,xlt=1b x+2,x >1 is differentiable at x=1

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

The value of b for which the function f(x)={5x-4,0xlt=1 , 4x^2+3b x ,1< x <2 and continuous at x=1

If f(x)={(x","xle1,),(x^2+bx+c",",xgt1):} then find the values of b and c if f(x) is diferentiable at x=1.

If the function f(x)={A x-B ,xlt=1 3x ,1

If f(x)=[x+1,\ xlt=1 ,3 -a x^2,\ x >1 is continuous at x=1 then find the value of adot

Discuss the continuity of the function f(x)={x , 0lt=x<1//2 12 , x=1//2 1-x , 1//2

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)=m a xi mu m{x^3, x^2,1/(64)}AAx in [0,oo),t h e n f(x)={x^2,0lt=xlt=1x^3,x >0 f(x)={1/(64),0lt=xlt=1/4x^2,1/4 1 f(x)={1/(64),0lt=xlt=1/8x^2,1/8 1 f(x)={1/(64),0lt=xlt=1/8x^3,x >1/8