arianna1453
  • arianna1453
I will FAN. Please help with this calculus question.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
arianna1453
  • arianna1453
1 Attachment
jango_IN_DTOWN
  • jango_IN_DTOWN
for differentiability Lf'(x)=Rf'(x)
jango_IN_DTOWN
  • jango_IN_DTOWN
Here Lf'(3)=2.3=6 and Rf'(3)=m so we must have ,m=6

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arianna1453
  • arianna1453
Where does LF come from?
jango_IN_DTOWN
  • jango_IN_DTOWN
Lf'(x) means the left hand derivative of f at the point x
jango_IN_DTOWN
  • jango_IN_DTOWN
and Rf'(x) means the right hand derivative of f at the point x
arianna1453
  • arianna1453
so for mx+b you would plug in 3 for x
jango_IN_DTOWN
  • jango_IN_DTOWN
no....
arianna1453
  • arianna1453
Wait... yeh ignore that. Sorry. Im super confused.
jango_IN_DTOWN
  • jango_IN_DTOWN
when x<=3, f(x)=x^2 and f'(x)=2x
jango_IN_DTOWN
  • jango_IN_DTOWN
when x>3, f(x)=mx+b and f'(x)=m
jango_IN_DTOWN
  • jango_IN_DTOWN
right??
arianna1453
  • arianna1453
Oh the derivatives of each. Okay i see now. right,
jango_IN_DTOWN
  • jango_IN_DTOWN
Lf'(3)=2.3=6 and Rf'(3)=m so both these must be equal for the function to be differentiable at x=3, so 6=m
jango_IN_DTOWN
  • jango_IN_DTOWN
and here b can take any real value. it has no restriction
arianna1453
  • arianna1453
Okay I understand that now, except for the b. Finding b. How is it any real value if its being added to m. and m is 6.
jango_IN_DTOWN
  • jango_IN_DTOWN
the differentiability has no relation with b here.. since f'(x) doesnot contain any thing related to b. so b can be any value,
jango_IN_DTOWN
  • jango_IN_DTOWN
@arianna1453
arianna1453
  • arianna1453
Okay. I think I have to find an actual value of b.
jango_IN_DTOWN
  • jango_IN_DTOWN
there will be no actual value. you take any place and place it for instance
jango_IN_DTOWN
  • jango_IN_DTOWN
oh wait a bit i think i have the answer
jango_IN_DTOWN
  • jango_IN_DTOWN
@arianna1453
jango_IN_DTOWN
  • jango_IN_DTOWN
see the function will be differentiable, so it will be continuous as well
jango_IN_DTOWN
  • jango_IN_DTOWN
now since we know the value of m, let us re-write the function
arianna1453
  • arianna1453
6x+b but b=-9 so its 6x-9 when x >3
jango_IN_DTOWN
  • jango_IN_DTOWN
f(x)=x^2,x<=3 f(x)=6x+b,x>3 now the left hand limits at x=3 is 3^2=9 and the right hand limit at x=3 is 18+b so 9=18+b so b=-9
arianna1453
  • arianna1453
And x^2 and 6x-9 connect together when graphing.
arianna1453
  • arianna1453
Good, we both got it now. ahaha.
jango_IN_DTOWN
  • jango_IN_DTOWN
hence we have m=6,b=-9
arianna1453
  • arianna1453
Right. Agreed

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