Instructions: . Read Chapter 3, pages 215-289, sections 3.1, 3.2, 3.3, 3.4, and 3.5 reading the definition of derivative, slope of tangent line, rate of change, differentiation rules and to draw a graph of a derivative function from the given function Herman, E. & Strang, G. (2020). Calculus volume 1. OpenStacks. Rice University. Provide your answers to the following problems. Write each step clearly when you answer each question. 1. Using the limit definition of derivative, find / (3) for the function f(x) = x3 +17x2 - 12x + 2 2. Find the slope of the secant line between the values 3 and 4 for the function f (2) = a 3. Applying limit definition of derivative, find the slope of the tangent line J (2 ) = *at x=3 4. What do you understand from question numbers 2 and 3 about secant lines and tangent lines? Explain any difference or any similarity. 5. The total cost of producing x winter jackets in dollars is given by () = 100 + 10x + 0.2x2 using the limit definition of the derivative, find average cost per jacket in [10,12]. Then find the average cost of making 1500 jackets. 6. Apply the derivative rules, find f (x) for f (x) = (x + 2)(x2 + 16x + 4) 7. Apply the derivatives rules, find f'(x) for f (x) = 21-5x312x2-5 8. Find the equation of the tangent line to the graph of f (x) = (x + 2) (x3 - 5x - 1) at x=1. 9. Use Desmos graphing calculator to graph the function f (x) = (x + 2)(x3 - 5x - 1) 10. The concentration of antibiotic in the bloodstream t hours after being injected is given by the function C(t) is measured in milligrams per litre of blood. Find the rate of change of C'(t) = 1+4 2t .Determine the rate of change for t=2 hours