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Text Elements
f(x) =
2
x
- 3x
find equation of slope at x = 4
pt 1. Get slope
f(h+x) - f(x)
h
f(h+4) - f(4)
h
=
(h+4) +3(h+4) - (4) - 3(4)
h
=
2
2
h + 8h + 16 +3h + 12 - 16 - 12
=
2
h
h + 11h
=
2
h
h + 11
=
lim
h
0
lim
h
0
lim
h
0
lim
h
0
lim
h
0
lim
h
0
= 11
pt 2. Get y-intercept
The slope equation must hit the same point on the original equation
( x, f(x) ) = (4, 28)
y = mx + b 28 = 11(4) + b b = -16
pt 3. Final equation
y = mx + b
y = 11x - 16