### Chapter 3 Review

AP Calculus
Mr. Manker

Difference quotient definition. Finds
derivative at a point.
−()
 lim
−
→
ℎ
ℎ

Write the equation of the tangent line to f(x)
at x = 2 if   = 3 2 + 7

Write the equation of the tangent line to f(x)
at x = 2 if   = 3 2 + 7

Use slope-intercept form: y – y1 = m(x – x1)
f(2) = 19, so (2, 19) is a point on graph
Use derivative to find slope of tan. at x = 2.

f’(x) = 6x  6(2) = 12

y – 19 = 12(x – 2)


 Is
= 7 − 4 + 7 increasing or
decreasing at x = 1?
2

Is   = 7 3 − 4 + 7 increasing or
decreasing at x = 1?
Rate of change, so find derivative at
x = 1:
2
 f‘(x) = 21 – 4
f’(1) = 17


The derivative is positive, so the
graph is increasing at x = 1.


Find f’(2) if f(x) = ln x.
We don’t know how to find the derivative of
this!!



nDeriv(ln x, x, 2) ≈ .500
To graph equation of derivative, replace x
value of 2 with variable:
nDeriv(ln x, x, x) (Good way to check your
derivatives!)

= 3 2 − 4 + 7
+ℎ −()
 lim
ℎ
ℎ→0
“forward difference quotient”
+ ℎ − ()
lim
ℎ→0
ℎ
3( + ℎ)2 −4  + ℎ + 7 − (3 2 − 4 + 7)
= lim
ℎ→0
ℎ
2
2
3 +6ℎ+3ℎ −4−4ℎ+7−3 2 +4−7
= lim
ℎ→0
ℎ
= lim 6 + 3ℎ − 4 = 6 − 4
ℎ→0





= 5 3 − 7 + 1
Derivative of displacement is velocity:
= 15 2 − 7
Derivative of velocity is acceleration:
a(t) = 30t

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