How Do You Simplify f(x+h) for f(x) = x^3 - 7x^2 + x + 1?

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To simplify f(x+h) for the function f(x) = x^3 - 7x^2 + x + 1, one must substitute x with (x+h) in the equation. This results in f(x+h) = (x+h)^3 - 7(x+h)^2 + (x+h) + 1. After substitution, the next step involves expanding and simplifying the expression. Some participants noted that this process is crucial for evaluating limits, but it was clarified that the original function must be subtracted from the expanded form to find the derivative. The discussion emphasizes the importance of careful substitution and simplification in calculus.
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Homework Statement



evaluate f(x+h) expand and simplfy f(x)=x^3-7x^2+x+1?


Homework Equations


f(x+h)


The Attempt at a Solution


my attempt (f(x+h)+f(x)+1
x^2(x+h)+x+1
x^2(x+7)+x1
im lost I'm not sure how to do this
 
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Replace the x's with x+h and simplify.
 
LCKurtz said:
Replace the x's with x+h and simplify.

o really so is it like

f(x)=(x+h)^3-7(x+h)^2+(x+h)+1
then I simplify
 
psp101 said:
o really so is it like

f(x)=(x+h)^3-7(x+h)^2+(x+h)+1
then I simplify

Yes.


J-Girl said:
yeah but the original equation is usually set up at(when u are evaluating the limit) (x+h)-f(x), so you have to minus the original function from the (x+h)^3-7(x+h)^2+(x+h)+1, you will just end up with the first derivative.

No you won't. There is more to it than that, and that's not what psp101 asked anyway.
 
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