Calculus Exam Part B Throughput the wn'tten exam. be sure to show proper form. Only solutions showing proper notation and complete solutions will receive full marks, All final answers should be simplied. with no negative exponents Within 60 minutes of opening this exam file, your answers need to be submitted to the assignment folder as a pdf. Ensure all answers are clear and you have uploaded all pages. hg Answer 1. State the derivative of each function. {6 marks} a) m = b) y = b' C) MI] = x" d) y = tam: e) y = mar) f) fix) = % 2. Complete each statement by placing the correct word into each blank. Use appropriate vocabulary and notation. {5 marks} a) This non-zero function in the form y = f(x) has the property : i I! 3")\" =Y- b) At the point where x = 1 , the function for} = x3 2x3 3x is and (increasing l decreasing) (concave up or concave down). c) The instantaneous rate of change of a function at a point where x = a corresponds to the slope of the at that point and can be found by evaluating the of the function at that point. 3. Find the derivative of each by showing your work. Express your answer in simplied, factored form with no negative exponents. {6 marks} a) y=(5")x3 b) hix)=cos3(3x 1') 4. Find the derivative of f(x) = L45\" and then evaluate f' (In 4). {3 marks} Long Answer 1. Use first principles to find the derivative of the function: f(x) = 3,-5 . (3 marks} 2. Evaluate the limit, if it exists lim x-0 + 1-1 . {3 marks} X3' {4 marks] Find the equation of the tangent to the graph of the function if = -2Sin(3x) at the point where x = g _ 4. A rectangular pigpen will be enclosed using one side of a farmer's barn and white vinyl fencing on the remaining 3 sides. The area is expected to be 6125ft2 and the cost of the vinyl fence is $30Ifoot. You have been asked to use your knowledge of optimization to determine the dimensions that would yield the minimum cost of this project, while maintaining the indicated area. Describe the steps and formulas you would use to model this problem using calculus. YOU DO NOT NEED TO actually SOLVE THIS! {3 marks}