victoriamaya864
victoriamaya864 victoriamaya864
  • 23-02-2020
  • Mathematics
contestada

1. Consider f(x) = 3x - 5
Find f(x+h)-f(x)/ h
(Difference Quotient) please show work and answer.​

Respuesta :

skyluke89
skyluke89 skyluke89
  • 01-03-2020

Answer:

3

Step-by-step explanation:

Here we have the function

[tex]f(x)=3x-5[/tex]

We want to find the following ratio:

[tex]\frac{f(x+h)-f(x)}{h}[/tex]

Note that the limit of this for [tex]h\rightarrow 0[/tex] is equivalent to the derivative of the function.

Here we have:

[tex]f(x+h)=3(x+h)-5=3x+3h-5[/tex]

And

[tex]f(x)=3x-5[/tex]

Therefore we have

[tex]f(x+h)-f(x)=3x+3h-5-(3x-5)=3h[/tex]

And therefore,

[tex]\frac{f(x+h)-f(x)}{h}=\frac{3h}{h}=3[/tex]

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