Lukecrayonz
  • Lukecrayonz
Derivs http://gyazo.com/da79c8768e1e4ff28a282298e1a5d458
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Luigi0210
  • Luigi0210
Oh darn! I've done these before but I forgot D:
Lukecrayonz
  • Lukecrayonz
I know that m=6 by finding the deriv and inputting 1
Lukecrayonz
  • Lukecrayonz
3x^2, bring down 2, subtract 1, deriv=6x

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More answers

Lukecrayonz
  • Lukecrayonz
6*1=6=m
Lukecrayonz
  • Lukecrayonz
y=mx+b, y=6x+b
Lukecrayonz
  • Lukecrayonz
So how to find b..
Lukecrayonz
  • Lukecrayonz
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
what is f(1)
Lukecrayonz
  • Lukecrayonz
Oh god, the one & only Jim thompson is here :D
Luigi0210
  • Luigi0210
;-;
Lukecrayonz
  • Lukecrayonz
6
jim_thompson5910
  • jim_thompson5910
you sure?
Lukecrayonz
  • Lukecrayonz
? How would it not be?:O
Lukecrayonz
  • Lukecrayonz
WAIT ITS 3
jim_thompson5910
  • jim_thompson5910
f(x) = 3x^2 when x >= 1 so f(1) = ???
jim_thompson5910
  • jim_thompson5910
good
Lukecrayonz
  • Lukecrayonz
I was using the deriv. to find it, not the original equation
jim_thompson5910
  • jim_thompson5910
so this means that the point (1,3) is on the function
jim_thompson5910
  • jim_thompson5910
for the function to be differentiable, it must be continuous
jim_thompson5910
  • jim_thompson5910
so what does that mean?
Lukecrayonz
  • Lukecrayonz
So now using the deriv for f'(1), y=6x+b, input (1,3) into it and solve for b?
jim_thompson5910
  • jim_thompson5910
for it to be continuous, the piece mx+b must be equal to 3 when x = 1, ie y = mx+b 3 = m(1) + b 3 = m + b in addition, when a function is differentiable, the slopes of the tangent lines of the function all exist and the slopes themselves make up a continuous function what this means is that for this to be possible, the slope m must be 6 since you've shown that the slope of the tangent line at x = 1 is 6 (when you used the derivative of f(x) = 3x^2) so m = 6 and you use this and 3 = m + b to find b
Lukecrayonz
  • Lukecrayonz
So then 3=6*1+b, 3=6+b b=-3?
Lukecrayonz
  • Lukecrayonz
YES ITS RIGHT I LOVE YOU JIM
jim_thompson5910
  • jim_thompson5910
very good, so m = 6, b = -3 making your first piece to be 6x - 3

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