NAME: DATE: MCV4U - Unit 3: Deriving Transcendental Functions Complete the Reference Declaration section below. If you used any references beyond the course text and lectures (such as other texts, discussions with colleagues or online resources), indicate this information in the space below. Declared references (Name, type of source/relation, etc...): Part A: Multiple Choice. Please answer the following MC questions on the GOOGLE FORM bubble sheet (not here). 1. What is the derivative of f (x) = e2x - e-2x ? a. f'(x) = 2e2x - 2e-2x f'(x) = e2x + e-2x b. f'(x) = e2x - e-2x f'(x) = 2e2x + 2e-2x 2. Determine the x coordinate of the point for which the tangent is horizontal to the function f (x) = =. a. In 2 NIN b. In 2 3. If f (x) = e-*", calculate f' (2). a. Ave C b. - - Ve 4. What is the derivative of f (x) = 3-6x+6 ? a. f'(x) = -6(3-6x+6) In3 f'(x) = -6(3-6x+6) In6 b. f'(x) = (3-6x+6) In3 C. f'(x) = (3-6*+6) In6 5. What is the derivative of f (x) = sin3(x2) ? a. f'(x) = 3sin?(x2) f'(x) = 6xsin2(x2) cos(x2) b. f'(x) = 3sin?(x2) cos(x2) f'(x) = 2xsin?(x2)NAME: DATE: 6. If f(x) = e2x - cos x, f'(x) is: a. f'x) = 2ex + tan x d f'x) = 2e2x + sin x b. f'x) = 2e2x + cosx f'x) = 2e2x - sin x 7. If f (x) = sin 5x, f'(x) is: a. f'(x) = -5 cos 5x f' (x) = 2 sin 5x b. f'(x) = -2 sin 5x di f' (x) = 5 cos 5x 8. Determine the slope of the tangent to the graph y = 3* at x =1. a. 3 In 4 C. 4 In 4 b. 4 In 3 d. 3 In 3 9. Determine the slope of the tangent to the graphy = e* at x =1. a. b. 4 2 10. A population of 100 bacteria doubles every 30 minutes. Use this information to find an expression for this population growth. Let P represent the population and t represent time in minutes. a. P = 100 (430) C. P = 30 230 b. P = 100 (330) d. P = 100 (230)NAME: DATE: Part B: Short Answer. Show ALL work for full marks. 11. Differentiate the following functions. Simplify when possible. ) y = ;ecos(4x+l) b) y = sin(Vx)In(4x + 3) Hint: Try to simplify using log rules before deriving. o y=log NAME: DATE: 12. Determine the 1317th derivative of the following functions. You MUST show work by finding at least the first 4 derivatives. a) f(x) = 22x1 b) f(x) = %cos(? 4x) 13. The voltage of a wall socket after t seconds is represented by V(t) = 75sin(90t - 4). Determine an expression for all the infinite minima's, using 1** and 2" derivatives. NAME: DATE: 14. A radioactive substance decays such that after t years, the amount of the substance remaining is expressed as N = Ng(1.7)'t. a) Use exponent and logarithm laws to convert the equation into the half-life equation. Note: 2 would be the base. b) Use exponent and logarithm laws to convert the equation into the general decay equation. Note: \"e\" would be the base. c) Using your solution from part b), find the rate of decay after 100 days. 15. Use implicit differentiation find the derivative for the following. Remember to isolate the derivative! You do NOT need to express v in terms of x. Leave all answers in exponent form (ex. = = x'and vy = y1/2) after simplifying. a) x2y + _+6=5 b) tan 3y + -x2y2 - cos xy = -V2y\fX MCV4U Summer... MCV4U Summer - July 2024 Monday Tuesday Wednesday Thursday Friday July 1 2 3 4 - 1 st Day of Class 5 A - Course Intro A-0.4 Limits & Continuity B -0.1 Avg Rates of Change B- 1.1 Deriving Polynomials C-0.2 Inst Rates of Change C-1.2 Product Rule D-0.3 Newton's Quotient D - Unit 0 Assessment: Rates of Change 8 10 11 12 A- 1.3 Displacement, Velocity, & A -2.1 First Derivatives & A-2.4 Deriving Rational Functions A - Unit 2 Assessment: A - 3.4 Deriving Exp Functions Acceleration Increasing/Decreasing B-2.5 Curve Sketching Curve Sketching B - 3.5 More Exp Derivatives B - 1.4 Quotient Rule B - 2.2 Maximum & Minimums C-2.6 Optimization B-3.1 Deriving Trig Functions C-3.6 Deriving Log Functions, & C-1.5 Chain Rule C-2.3 Second Derivatives & D - 2.6 Optimization Cont. C-3.2 More Trig derivatives Implicit differentiation D - 1.6 Applications: Concavity D -3.3 Application of Trig -3.7 Exponential Modelling Rate of Change D - Unit 1 Assessment: Derivatives Derivatives Cutoff for Midterms 15 16 17 18 19 A - Unit 3 Assessment: A -4.4 Physics Applications A-5.2 Dot Product A- 5.5 Cro Product A-6.2 Line Transcendental Functions B -4.5 Vector Components 8 -5.3 App rcatron" B -4.1 Intro to Vectors C-5.1 Cartesian Vectors C-5.4 of ply Form C-4.2 Vector Addition D -Work Period D D - 4.3 Vector Multiplication ectors 22 23 24 - Unit 6 Asses final Attendany B -6.8.. Planes Lines and Planes in 3D 8 Int. of 3 Planes Cor ment Conta. ment conte Have a great rest of D - on Goop Meet D- Work Period wap Up Summer in August