Question

Thank you for your help :)
"The piecewise function



f(x)= n(x^3)-x______when____x<(or=to)1
=m(x^2)+5_______when_____x>(or=to)1


is differentiable everywhere. What is n?




If you could explain step by step how to do this that would be great because I just do not see how to do this problem...thank you

Answer 1

is it continous, and is f' continous
f(1)=n-1
g(1)=m+5, or m+5=n-1 or m=n-6

f'=3nx^2
f'(1)=3n
g'=2mx
g'(1)=2m
so continous means 2m=3n or 2n-12=3n
n=-12

check my work.