6. Consider the family of functions given by f (x) = kx\" k2x2 + h + l . Find the value of It so that f (x) has an inection point at x = 2 'r'. A rescued whale is released in the ocean 300 meters due east of a coast guard station. If the whale swims directly away from the shore. How fast is the angle 9 (from the observer at the Coast guard station) changing when the whale is 400 meters from the coast guard station and at that moment is traveling at a rate of 40 meters per minute? Give an exact answer, then approx. in your sentence. Coast guard station point of release hale 5. Let f (x) = .1:3 3a2x + 2a\" with the parameter a > 1. The graph of f (x) is given below. Each box represents a place where a value for the axes belongs. Fill in the ve boxes with the correct values. (Your answers will involve a.) Must show work to support your values. Instructions: For questions 5, 6 and 7 to receive full credit you must use the methods taught in our calculus class. Show your work which will justify your answer. You may use your calculator to verify your answers. You may use notes, solutions, calculator, and textbooks. You may not ask for help or search for help. It is what you know using our class material. 1. Match the following three theorems to the correct statement that corresponds to the theorem about the function f. No written justification required. A. Mean Value Theorem B. Intermediate Value Theorem C. Extreme Value Theorem If f (x) is continuous on the interval [a, b] and differentiable on (a, b), 1) There must be at least one global maximum and global minimum on the interval [a, b]. ii) For every number, k, between f (a) and f (b) then there exist at least one number c, with a 0 for all x then f is monotonic. T F f is differentiable everywhere. An inflection point can also be a local max or min. T F f is differentiable everywhere. On the interval [a, b] there will be a global max and min. T F If the radius, R , of a circle is increasing at a constant rate, then the circumference, C, of that circle is also increasing at the same constant rate. T F If the radius, R , of a sphere is increasing at a constant rate, then the volume, V, of that sphere is also increasing at the same constant rate. T F If y = x then dy = dx T F A function may have infinitely many critical points. T F g(x) is a continuous function, a local maximum or minimum can occur when g'(x) is undefined