hybrid function question help

[lilaznkev1n]

Hi

Need help on approaching this question. Don't know where to start

Given the function:
                                             {  a[squareroot(x+2)]   for x greater and equal to 2
                                   f(x)=   l
                                             {  mx + 3                    for x less than 2
                           Find the values of a and m, if f is a differentiable function. [4 marks]
Any help is greatly appreciated
Thanks

[Whatlol]

if the function is differentiable then a(root(x+2) = mx+ 3 for x = 2 .: 2a=2m+3
and also d/dx(mx+3) = d/dx (a(root(x+2)) for x= 2
so m = a/2(root(x+2)) for x=2
so m= a/(4)
4m=a
sub that back into the first equation
8m=2m+3
6m=3
m=1/2
therefore a =2

[lilaznkev1n]

thank you so much