Hi Tsum S
-h -2x +5 is the difference quotient for f(x) = 5x -x2
Please see below
f(x) = 5x - x2
Can be written as
f(x) = -x2 + 5x
Then you just to plug it into the difference quotient give as follows:
f(x + h) - f(x)/(h)
To find f(x + h), plug in x + h instead of x
(-(h + x)2 + 5(h + x)) - (-x2 + 5x)/(h)
Then just multiply and combine like terms
(-(h2 +2hx + x2) + 5h + 5x ) - (-x2 + 5x)/(h) = (-h2 -2hx -x2 +5h + 5x) +x2 -5x/(h) =
-h2 -2hx - x2 +5h +5x + x2 -5x/(h) = h2 -2hx + 5h/(h) = h(h - 2x + 5)/(h) = h - 2x + 5
Notice above the x2 , 5x cancel out, when factor out the h then the h in the denominator divides out
Note the h in the denominators may not line up correctly upon submission but if you write this out yourself you will exactly where they should be. I put them as, /(h), so hopefully they will not shift out of place
I hope you find this useful if you have any questions just send me a message
