Evaluate the following function at the values x+1 and x+h and find f(x+h)-f(x)/h

Question

anonymous · Answer

so... f(x+1)=

anonymous · Answer

oops, forgot to mention the main equation of f(x)=xsquared+5

anonymous · Answer

Plug x+1 into the function f(x) = x^2 + 5 that is take the x + 1 and put it where the x is.
                                  f(x+1) = (x+1)^2 +5 
Foil the (x+1)^2.  Add 5 to simplify.
Now do the same with the x+h.

anonymous · Answer

so f(x+1)=xsquared-5x-5?

anonymous · Answer

Not quite, but almost!  (x+1)(x+1)-5 = x^2 +2x +1 - 5
which equals what?

anonymous · Answer

$$x ^{2}+4x-4?$$

anonymous · Answer

Good! now you're going to plug in x + h just like you did the x + 1.

anonymous · Answer

okay, thank you!

anonymous · Answer

Did you get x^2 + 2xh + h^2 - 5 ?

anonymous · Answer

Finally the last bit.  [f(x+h) - f(x)]/h = [x^2 + 2xh + h^2 -5 - (x^2 - 5)]/h
 Run the negative through the x^2 - 5 then simplify the numerator. You'll find that when you factor out the common h then you can cancel the h in the denominator.  This is the precursor to limits in calculus so make sure you understand this concept thoroughly before continuing!