Differntiability question

[SoniaKapoor]

Find values a and b so that the fn f(x)={x^2+3x+a    if x<=1
                                                     {bx+c           if x>1
is differntiable at each x belongs to R.

[The Villain]

I'm getting a=3 and b=5

[RajEco]

how did you get a ?

[SINGHAM]

Yes, I have the same question, too!

[Homer Simpson]

I am getting a = -5 and b = 1-c

[SoniaKapoor]

I typed it wrong ..it should be ax+c..

[The Villain]

then the answer is surely a=3,b=5

[Homer Simpson]

Sonia, can you please clarify something? is Left hand part, x whole raised to the power 2+3x+a or x square plus 3x+a?

[The Villain]

Tsuki...i dont think it is whole square..

[Anjali]

@Ron please explain the approach !

[Anjali]

@ron please explain

[The Villain]

Sry Anjali for the late reply.Didnt notice it..
For this quest you have to find both left hand and right hand continuity and equate it.Do the same for left hand derivative and right and derivative.You'll get 2 equations.Solve it .You will get the reqd values. :))

[Homer Simpson]

thank you Ron :)

[Anjali]

Ron Iam getting b as 5. Not able to find a. Please guide.
And since its differentiable , so it must be continuous - that makes sense , but why are we equating left and right hand derivatives ?

[Homer Simpson]

hi, i tried it again and this time, i got a=5 and c=4

taking the problem as (after correction mentioned)

f(x)={x^2+3x+a    if x<=1
       {ax+c           if x>1

We equate LHD and RHD for derivative to exist at x=1

Please let me know if this is fine.

[The Villain]

@Sonia...pls post the quest again..i guess the 2nd fn should be bx+2

[Anjali]

Yes Ron , coz then how will we get away with c ?

[SoniaKapoor]

x^2+3x+a
and bx+2
sry guys...my bad

[Anjali]

Thank you ! Got the answer !