Thinking 17. The population of foxes, in thousands, in a provincial park has been modelled using the 50ln(t+1) equation P(t) = t+1 where t is the time in years. Determine the maximum population of foxes. 18. Determine the coordinates of the absolute extremes of y = 3sinx(cosx), 0 ≤x≤2л. [ | | | 8. Given f(x) = sin (4x + 7/7), find f' (Z). a) 0 b) 4 9. The derivative of y = √√ex is: a) √ex 1 b) 2√e c) -4 d) 1 d) √√√ex b) 3e (cosx)(sinx) c) 3e* (cosx-sinx) d) 3e cosx+3e sinx 10. The derivative of y = 3e*cosx a) 3e*sinx Communication True or False: [' 11. The derivative of a sinusoidal function is another sinusoidal function. 12. The rate of change of a sinusoidal function is periodic in nature. 13. A sinusoidal function can be differentiated only if the independent variable is measured in radians. 14. The derivatives of the reciprocal trigonometric functions can be found using the chain rule and their related base functions. 15. There are an infinite number of tangents with a given non-zero slope to a sinusoidal curve. sinx 16. Using the Quotient tanx = to prove tanx = sec²x. [3 Marks] COSX dx

Thinking 17. The population of foxes, in thousands, in a provincial park has been modelled using the 50ln(t+1) equation P(t) = t+1 where t is the time in years. Determine the maximum population of foxes. 18. Determine the coordinates of the absolute extremes of y = 3sinx(cosx), 0 ≤x≤2л. [ | | | 8. Given f(x) = sin (4x + 7/7), find f' (Z). a) 0 b) 4 9. The derivative of y = √√ex is: a) √ex 1 b) 2√e c) -4 d) 1 d) √√√ex b) 3e (cosx)(sinx) c) 3e* (cosx-sinx) d) 3e cosx+3e sinx 10. The derivative of y = 3ecosx a) 3esinx Communication True or False: [' 11. The derivative of a sinusoidal function is another sinusoidal function. 12. The rate of change of a sinusoidal function is periodic in nature. 13. A sinusoidal function can be differentiated only if the independent variable is measured in radians. 14. The derivatives of the reciprocal trigonometric functions can be found using the chain rule and their related base functions. 15. There are an infinite number of tangents with a given non-zero slope to a sinusoidal curve. sinx 16. Using the Quotient tanx = to prove tanx = sec²x. [3 Marks] COSX dx

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 35E

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