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math

posted by on .

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

  • math - ,

    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.

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