1. ## Are these correct?

1) Find f(2+h), f(x+h), and (f(x+h) - f(x))/h
f(x)= x/(x+1)
f(x+h)= (x+h)/(x+h+1)
(f(x+h) - f(x))/h= 1/[(x+1)(x+h+1)]

2) The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and$4800 to produce 300 chairs in one day.
(a) Express the cost as a function of the number of chairs produced, assuming that it is linear.
(b) what is the slope of the graph and what does it represent?
(c) what is the y-intercept of graph and what does it represent?
(a) c(x)=13x+900
(b) slope is 13 which represents the price to produce each chair
(c)the y-intercept is 900 which represents the cost function when x=0

2. Originally Posted by yoman360
1) Find f(2+h), f(x+h), and (f(x+h) - f(x))/h
f(x)= x/(x+1)
My answers: f(2+h) = (2+h)/(3+h) CORRECT!
f(x+h)= (x+h)/(x+h+1) CORRECT!
(f(x+h) - f(x))/h= 1/[(x+1)(x+h+1)]
$\displaystyle \frac{f(x+h) - f(x)}{h}$
\displaystyle \begin{aligned} &= \frac{\frac{x + h}{x + h + 1} - \frac{x}{x + 1}}{h} \\ &= \frac{\frac{(x+h)(x + 1) - x(x + h + 1)}{(x + 1)(x + h + 1)}}{h} \\ &= \frac{\frac{x^2 + hx + x + h - x^2 - hx - x}{(x + 1)(x + h + 1)}}{h} \\ &= \frac{\frac{h}{(x + 1)(x + h + 1)}}{h} \end{aligned}
\displaystyle \begin{aligned} &= \frac{h}{(x + 1)(x + h + 1)}\cdot \frac{1}{h} \\ &= \frac{1}{(x + 1)(x + h + 1)} \end{aligned}

CORRECT!

01

3. Thanks!

4. Originally Posted by yoman360
1) Find f(2+h), f(x+h), and (f(x+h) - f(x))/h
f(x)= x/(x+1)
f(x+h)= (x+h)/(x+h+1)
(f(x+h) - f(x))/h= 1/[(x+1)(x+h+1)]

2) The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and$4800 to produce 300 chairs in one day.
(a) Express the cost as a function of the number of chairs produced, assuming that it is linear.
(b) what is the slope of the graph and what does it represent?
(c) what is the y-intercept of graph and what does it represent?