Mcv4u - unit 2 lesson notes Calculus (St. Francis of Xavier Catholic Secondary School)

Mcv4u - unit 2 lesson notes


Calculus (St. Francis of Xavier
Catholic Secondary School)

,MCV 4U Calculus and Vectors

St. Francis Xavier Catholic Secondary School
Department of Mathematics
MCV4U

UNIT 2 - DERIVATIVES


LESSON TOPIC ASSIGNED QUESTIONS
P. 83 #1, 2bdfh, 3abf, 4aef,
1 2.1 Derivative of a Polynomial Function 5a, 6ad, 11, 13ab, 17ab, 27
P. 93 #2ace, 3ac, 4a, 5ad,
2 2.2 The Product Rule 6ac, 7ac, 9cd, 11, 13a, 14
P. 118 #3ac, 4ac, 5ac, 7ac,
3 2.4 The Chain Rule 9, 10, 12, 15, 16, 17, 19
Mid-chapter review
4 Quiz: Sections 2.1 – 2.4

P. 124 #1ac, 2ac, 3ac, 4ac,
5 2.5 Derivatives of Quotients 5ac, 6bd, 8, 9, 10
P. 138 #4, 5, 8, 16, 18
6 2.6 Rate of Change Problems
P. 142 #1, 2a, 3, 4, 5, 6abcd,
7 Review 7,
9, 10, 11, 12, 13
P. 144 #2, 3, 7, 9, 10

8 UNIT 2 TEST

, MCV 4U Unit #2 - Lesson #1

2.1 – DERIVATIVE OF A POLYNOMIAL FUNCTION

Learning Goal: I can determine the derivative of a polynomial function


Recall: The derivative of a function is equal to the of a tangent line for any value of x.


5 DIFFERENTIATION RULES:

RULE LAGRANGE NOTATION EXAMPLE
f(x) = 4
Constant Rule
f ’(x) = 0
If f(x) = c , where c is a
constant, then…
f(x) = x3
Power Rule f ’(x) = nxn-1
If f(x) = xn , then…
f(x) = 2x3
Constant Multiple Rule
If f(x) = c(g(x)) for any constant f ’(x) = cg’(x)
c, then…

h(x) = x3 + x
Sum Rule
If the functions f(x) and g(x) are
h’(x) = f’(x) + g’(x)
differentiable and h(x) = f(x) +
g(x), then…

h(x) = 3x - 2
Difference Rule
If the functions f(x) and g(x) are
h’(x) = f’(x) – g’(x)
differentiable, and h(x) = f(x) –
g(x), then…


Example: Determine the derivative of each function.

a) f(x)  3x4  2
x2 b) y  x 3  c) 𝑓(𝑡) = −4.9𝑡2 + 10
5x 3




𝑚
1= 𝑎−𝑛 𝑛
Recall: 𝑎𝑛
√𝑎𝑚 = 𝑎𝑛