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MCV4U Chapter 4 Practice Questions
1. Compute each limit.
a.
lim
3x 4 2x 3 10x
x
lim 2x 5 x 2
d. x 3x 5 3
lim
4
2
b. x 3x 3x x
lim x x 2
e. x 2 x 3
lim x 3 x
c. x x 2 3
f.
lim x 1
x 1 x 2 1
2. Find the local maximum and minimum points for
f (x) 3x 3 2x 2 .
4
3
2
3. Find the inflection points for f (x) x 6x 12x x .
2
4. Find the global maximum and minimums for f (x) (x 2) (x 3) over the interval [–1, 2].
3
2
5. Determine the constants a, b, c, and d, so that the curve defined by y ax bx cx d has a
local maximum at point (2, 4), and a point of inflection at the origin.
3
2
6. Sketch the graph for f ( x) x 3x 9 x .
Domain:
x and y-intercepts:
Symmetry:
Asymptotes:
First Derivative:
Sign chart for f (x ) :
x
f(x)
f (x )
Local maximum and minimum:
Second Derivative:
Sign chart for f (x) :
x
f(x)
f (x)
Point of inflection:
Graph sketching:
7. Sketch the behaviour of the function
f (x)
x
x x 6
2
near each asymptote.
8. Find the points of inflection for:
f (x)
2x
x2 4
2x 2 x 1
9. Find the horizontal asymptote(s) for f (x)
2x
10. Find the critical numbers for
1
3
f (x) x x 2
2
3
Name: _____________________________
Date: ______________________________
MCV4U Quiz 4C: Chapter 4
K (30%)
A (30%)
/21
T (20%)
/21
/14
Total Mark:
(5x
x → −
lim
lim
(
4
− 4 x 3 − 32 x
)
b. x → − 5 x − 5 x − 3x
4
lim 3x 3 − 3x
c. x →
− 3x 2 + 5
/14
/70
[K – 6, C – 3]
1. Compute each limit.
a.
C (20%)
2
− 4 x 5 + 3x 2
d. x → − 5 x 5 − 5
lim
)
lim 3x − 3x 2
e. x →
4 − 3x 3
f.
lim 3x + 3
x → 1 3x 2 − 3
3
2
2. Find the local maximum and minimum points for 𝑓(𝑥) = 6𝑥 − 7𝑥 .
[K – 5]
3. Find the inflection points for𝑓(𝑥) = 4𝑥 4 − 9𝑥 3 − 45𝑥 2 + 4𝑥.
[K – 6]
4. Find the absolute maximum and minimum values for𝑓(𝑥) = (𝑥 + 5)2 (𝑥 − 6) in the interval [–4, 5].
[A – 7]
3
2
5. Determine the constants a, b, c, and d, so that the curve defined by y = ax + bx + cx + d has a
local maximum at point (5, 7), and a point of inflection at the origin.
[A – 7]
−𝑥
6. Sketch the behaviour of 𝑓(𝑥) = 𝑥 2 +𝑥−9 near each vertical asymptote.
−5𝑥
7. Find the points of inflection for 𝑓(𝑥) = 𝑥 2+7.
[K – 4]
[T – 6]
8. Find the horizontal asymptote(s) for𝑓(𝑥) =
2
√5𝑥 2 +𝑥+4
5𝑥
1
9. Find the critical numbers for𝑓(𝑥) = 𝑥 3 (𝑥 − 5)3 .
.
[T – 2]
[A – 7]
10. Sketch the graph of 𝑓(𝑥) = −4𝑥 3 + 6𝑥 2 + 32𝑥 by completing all the given components below:
[T – 6, C – 11]
Domain and Range:
x- and y-intercepts:
Symmetry:
Asymptotes:
First Derivative:
Sign chart for f (x) :
x
f(x)
f (x)
Local maximum and minimum:
Second Derivative:
Sign chart for f (x) :
x
f(x)
f (x )
Point of inflection:
Graph sketching:

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I was struggling with this subject, and this helped me a ton!