find the derivative of f

Question

f(x)=x²-4x+3

Answer 1

To start finding the derivative you can use the limit formula for derivatives: lim x -> 0 [f(x+h)-f(x)]/h

 

You need to then plug in x+h into the original function and subtract it by the original function and divide that by h. Simplify all of that and take the limit as h approaches 0. This is similar to plugging in 0 like in Algebra, with a few exceptions. It does not make sense to plug in  h into 0 until the very end, unlike in Algebra which you can guess and check that way. Not to mention that if you plugged in when you have an h/h, you would end up with a 0/0, which is indeterminate, which means that you may have cancelled something out too early with the 0.

 

lim x -> 0 [f(x+h)-f(x)]/h -> [(x+h)^2-4(x+h)+3 - (x^2-4x+3)]/h -> lim--> 0 (2xh+h^2-4h)/h =

2x+(h-->0)-4 =

YES DO THIS: 2x - 4 = the derivative

NO DON'T DO THIS: lim -->0 [(2x(h=0)+0^2-4(0)]/0 = 0/0

 

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You can double check your answer and you might not learn this for a while, using the Power Rule.

 

The power rule goes like this: df/dx (the first derivative) X^(n) = n(x)^(n-1)

 

You had  f(x)=x^2-4x+3, so using the power rule, you get, where for the first term: n=2 and the second term, n=1, AND I forgot to mention that the derivative of any constant (number without a variable) is 0.

 

Therefore: df/dx(x^2-4x+3) = (2)(x)(2-1) - 4x^(1-1) +0

 

That's it! Hope that helped!