SOLUTION: given: f(x)=5x-x^2 find: f(5-h)-f(5)/h

Algebra ->  Trigonometry-basics -> SOLUTION: given: f(x)=5x-x^2 find: f(5-h)-f(5)/h      Log On


   

Question 163395This question is from textbook Algebra and Trigonometry
: given: f(x)=5x-x^2
find: f(5-h)-f(5)/h This question is from textbook Algebra and Trigonometry

Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
given: f(x)=5x-x^2
find: f(5-h)-f(5)/h
-----
f(x) = 5*x - x^2
f(5-h) is gotten by replacing x with (5-h), so
f%285-h%29+=+5%2A%285-h%29+-+%285-h%29%5E2
-----
f(5) is gotten by replacing x with 5, so
f%285%29+=+5%2A5+-+%285%29%5E2
-----
since there is no parentheses around it, your formula f(5-h)-f(5)/h
is assumed to be:
f%285-h%29+-+%28f%285%29%2Fh%29
-----
if you meant %28f%285-h%29+-+f%285%29%29%2Fh, that would be a different equation.
-----
i'll solve for
f%285-h%29+-+%28f%285%29%2Fh%29
-----

this becomes
25+-+5%2Ah+-+%2825-10%2Ah+%2B+h%5E2%29+-+%28%2825-25%29%2Fh%29
which becomes
25+-+5%2Ah+-+25+%2B+10%2Ah+-+h%5E2+-+%280%2Fh%29
which becomes
5%2Ah+-+h%5E2
-----
as far as i can tell.
-----
if you really meant %28f%285-h%29+-+f%285%29%29%2Fh, then the equation becomes
%285%2A%285-h%29+-+%285-h%29%5E2+-+%285%2A5+-+%285%29%5E2%29%29%2Fh
which becomes
%2825+-+5%2Ah+-+25+%2B+10%2Ah+-+h%5E2+-+25+%2B+25%29%2Fh
which becomes
%285%2Ah+-+h%5E2%29+%2F+h
which becomes
5+-+h
-----
either way the key is to substitute (5-h) for x in f(5-h), and to substitute (5) for x in f(5)
-----