Derivatives Assignment 1. Find the derivative of each function. a. f(x) = 13x4 - 7x3 + 5x2 + 1la + 75 [2 marks] b. f(a) = (23 + 2x2 + 4) (24 - 3) [3 marks] c. f(x) = 3x2 6x47 Ar-1 + [3 marks] d. f(ac) = (4ac3 - 7ac) '[2 marks] e. 12 = y3 + 2 [4 marks] f. f(a) = 156 [1 marks] g. f(x) = (1 - 3x)2(x2 - 2) [3 marks] 2 h. f(a) = 2x2+1 [3 marks] i. f(x) = (2x - 3) (5 - x) (x2 + 2x -1) [4 marks] 2. Find f" for f(a) = (3ac2 - 7ac + 4) .[5 marks] 3. Find the third derivative of f(x) = 12x10 - 3x7 + 4x5 + 5x2 + 6. [4 marks] 4. Find the equation of the tangent line to the curve y = x - 2x + 3 at the point (5, 18). [5 marks]10. . Find the point on the parabola y = :L'2 + 3x + 4 where the slope of the tangent is 5, and graph the parabola and its tangent line using technology. [6 marks] . Give one example of a real-life positive rate of change, and one example of a real-life negative rate of change. Include approximate values and units. [4 marks] - Avehicle is described as travelling at 35 km/h. What are two ways this measurement could be interpreted? [4 marks] IV represents the volume of an object, what does % represent? [2 marks] . A construction worker accidentally drops a hammer from a height of 90 m while working on the roof of an apartment building. The height, 8, in metres, of the hammer after seconds can be modelled by the function s(t) =90 4.9t%, > 0. a. Determine the velocity of the hammer at 1 s and 4 s. [3 marks] b. When will the hammer hit the ground? [3 marks] c. Determine the impact velocity of the hammer. [3 marks] The motion of a particle is described by the position function (t) = 23 152 + 33t + 17, t > Owhere tis measured in days and s(t) in millimetres. a. When is the particle at rest? [4 marks] b. When is the velocity positive? [4 marks] c. Draw a diagram, or describe a diagram in words, to illustrate the motion of the particle in the first 5 days. [3 marks] d. Find the total distance travelled in the first 5 days. [3 marks] 10. 1. 12 13. 14. c. Determine the impact velocity of the hammer. [3 marks] The motion of a particle is described by the position function 8() = 2t3 152 + 33t + 17, t > Owhere tis measured in days and s(t) in millimetres. a. When is the particle at rest? [4 marks] b. When is the velocity positive? [4 marks] c. Draw a diagram, or describe a diagram in words, to illustrate the motion of the particle in the first 5 days. [3 marks] d. Find the total distance travelled in the first 5 days. [3 marks] A snowball melts so that its radius decreases by 0.2 cm/min. Find the rate at which the surface area decreases when the radius is 4 cm. (SA = 4:1?"2) [6 marks] _For the function f(z) = ax + bx? 5 + 9, determine the values of @ and b so that f(1) = 12 and F'(1) = 3. [5 marks] Determine the equations of two lines that pass through the point (-4, -5) and are tangent to the graph of iy = z2 +1 You may round coefficients to two decimal places. [6 marks] Two particles have positions at time given by 81 = 4t 2 and 89 = 5t2 3 When the acceleration of the two particles are equal, find the positions and velocities of both particles. [ marks]