Simplify the Differential Quotient | f(x) = 5x^2

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To simplify the differential quotient for the function f(x) = 5x^2, start by calculating f(x+h) as 5(x+h)^2. Then, find the difference f(x+h) - f(x) by subtracting 5x^2 from the result. This yields the expression that needs to be divided by h to complete the simplification. It's important to note that the limit as h approaches zero is necessary to obtain the derivative, but this step is not included in the current simplification process. The focus remains on simplifying the difference quotient itself.
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Simplify the differential qoutient like this (f(x+h)-f(x)) / h
and the qoute is f(x) = 5x^2

Please Help I don't know how to do this!
 
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Didn't you forget a limit for h going to zero? Put in the function then...
 
Izekid said:
Simplify the differential qoutient like this (f(x+h)-f(x)) / h
and the qoute is f(x) = 5x^2
Please Help I don't know how to do this!

You mean "difference quotient". You don't yet have a "differential" because, as TD said, you haven't taken the limit.

All we can say is "do what you are told!"

f(x)= 5x^2 so f(x+h)= 5(x+h)^2. Calculate that.
f(x+h)- f(x)= what you just did, minus 5x^2.

Last thing to do is divide by h.
 

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