Please help me out with this question

Calculus
Tutor: None Selected Time limit: 1 Day

Difference quotient f(x+h)-f(x) / h for y=4x-x^2 please show work

Jan 15th, 2015

I believe the question wants you to use y = 4x-x^2 as your function, f.


Therefore:
f(x+h) = 4(x+h) - (x+h)^2
f(x) = 4x-x^2

f(x+h) - f(x) / h
*PLUG IN above values
(4(x+h) - (x+h)^2) - (4x - x^2) / h
*EXPAND the squared polynomial and DISTRIBUTE negative
(4x + 4h - (x^2 + 2xh + h^2) - 4x + x^2) / h
*DISTRIBUTE negative
(4x + 4h - x^2 - 2xh - h^2 - 4x + x^2) / h
*COMBINE like terms
(4h - 2xh) / h
*DIVIDE by h
4 - 2x

Jan 15th, 2015

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