Sir John A. Macdonald Secondary School Calculus Worksheet

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Sir John A Macdonald Secondary School

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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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