Question

x2+3x+a,x<0
bx+2,x>1
find the value of a and b if it is differentiable at x=1

Answer 1

If the function is differentiable,then it should be continuous.
x2+3x+a,x<0
Differentiate above with respect to x.
The expression turns into 2x+3
then substitute x=1 (because it is differentiable at 1,i.e, continuous at 1)
then we get..whole value as 5

bx+2>1
repeat the above stated procedure.
differentiate with reference to x,we get b
then substitute x=1.As there is no x variable here,finally we get only b.

equate both the values.
b=5.