Answer
a. $100$
b. The production of wire is increasing by 100 feet per dollar spent for raw materials.
c. 0; When no money is spent for raw materials, no wire is produced.
Work Step by Step
(a)
$f(x)=100x=mx+c$
where m=slope
$\Longrightarrow$
m=slope=100
(b)
$\delta f(x)$=f(x+$\delta x$)-f(x)=100(x+$\delta x $)-100x
$\delta f(x)$=100(x+$\delta x $)-100x=100x+100$\delta x$-100x=100$\delta x$
$\delta f(x)$=100$\delta x$
$\frac{ \delta f(x) }{\delta x}=100$
$\Longrightarrow$
The production of wire is increasing by 100 feet per
dollar spent for raw materials.
(c)
Put x=0 in
$f(x)=100x$
$f(0)=100\times 0=0$
$\Longrightarrow$
When no money is spent for raw materials, no wire
is produced.
