anonymous
  • anonymous
f is a differentiable function on the interval [0, 1] and g(x) = f(4x). The table below gives values of f ′(x). What is the value of g ′(0.1)?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
https://gyazo.com/b435133c157b25d1c60f85c59cdeba34
anonymous
  • anonymous
Just multiplied by 4. Would that be right?
anonymous
  • anonymous
@zepdrix it's destiny telling you to help me ;P

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zepdrix
  • zepdrix
hehe
zepdrix
  • zepdrix
\[\large\rm g(x)=f(4x)\]Take derivative, apply chain rule on the right side of the equation.
zepdrix
  • zepdrix
Understand that step? :d
anonymous
  • anonymous
Chain rule on th eright side?
zepdrix
  • zepdrix
\[\large\rm \frac{d}{dx}f(4x)\quad=f'(4x)\cdot(4x)'\]Yes, chain rule. Multiply by the derivative of the inner function.
zepdrix
  • zepdrix
\[\large\rm g(x)=f(4x)\]Differentiate with respect to x,\[\large\rm \frac{d}{dx}g(x)=\frac{d}{dx}f(4x)\]Leading to\[\large\rm g'(x)=f'(4x)\cdot(4x)'\]this\[\large\rm g'(x)=f'(4x)\cdot(4)\]
zepdrix
  • zepdrix
Confused?
anonymous
  • anonymous
I got it just confused on how that'll help me.
zepdrix
  • zepdrix
Well we're looking for g'(0.1). Let's plug that into this relationship.\[\large\rm g'(0.1)=4\cdot f'(4\cdot0.1)\]\[\large\rm g'(0.1)=4\cdot f'(0.4)\]
zepdrix
  • zepdrix
And then use the table to finish the problem :o
anonymous
  • anonymous
Ohhhhhhhhhhhhhh Got it -16
zepdrix
  • zepdrix
Yay!
anonymous
  • anonymous
8/8 m8 that was gr8 thx
zepdrix
  • zepdrix
lol
anonymous
  • anonymous
Good job m8

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