jboling41 jboling41
  • 25-04-2019
  • Mathematics
contestada

Find the slope of the function -2x + 1 by the definition of limit.

a0

Respuesta :

LammettHash
LammettHash LammettHash
  • 25-04-2019

Let [tex]f(x)=-2x+1[/tex]. By definition, the derivative is

[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h[/tex]

So

[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{(-2(x+h)+1)-(-2x+1)}h=\lim_{h\to0}\frac{-2h}h=\lim_{h\to0}-2=-2[/tex]

and the slope of any line tangent to [tex]f(x)[/tex] is -2.

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