Alex R.

asked • 10/06/16

Use the definiton of a derivative to solve -2x+5

So far I have:
y=-2+5
 
y1 = (-2(x+h)+5-(2x+5))/h
 
(-2-2h+5-2x-5)/h
 
(-4x-2h)/h
 
If I set h=0 it becomes -4x/0 which is undefined... What am I doing wrong?
 
 

Peter G.

tutor
When you can't get the h in the denominator to cancel, look for algebra errors earlier on
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10/06/16

Alex R.

Found my dumb mistake... Thanks haha
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10/06/16

Kenneth S.

Alex, you omitted the x after coefficient 2 in your first line, and you used the digit 1 as an exponent; you should have written y' (using an apostrophe).
 
I strongly advise you to label, at each line of your work, as you simplify, what you are doing. That is, y' = ...
 
This is especially important because in some problems you'll be finding further derivatives, and work is confusing when all you have is a bunch of expressions without their being labeled (identified) as to what they are supposed to be.
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10/07/16

1 Expert Answer

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Arturo O. answered • 10/06/16

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Let us work this out step by step:
 
f(x) = -2x + 5
 
f(x + h) - f(x) = -2(x + h) + 5 - (-2x + 5)
 
Simplify and get
 
f(x + h) - f(x) = -2h
 
[f(x + h) - f(x)] / h = -2h / h = -2
 
You will get -2 for the derivative, which is the correct answer.
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Alex R.

Wow i'm stupid I forgot to add the minus sign to the 2 when I did it... Thanks! lol
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10/06/16

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