MAT 5 Calc e Calc 2 6-1 Module Six Discussion: Finding a Fmetion to Match a Remaining Time: Unlimitsd Shape For this week's discussion, you are asked to generate a continuous and differentiable function f (:t:) with the following properties n) : MAT-22 1 / 61 Module Six Discussion: Finding a Function to Match a Shape f(z)is decreasing at x = 5 f(z) has alocal minimum at z = 3 + f(z) has alocal maximum at z 3 Your classmates may have different criteria for their functions, so in your initial post in Brightspace be sure to list the criteria for your function. Hints: Use calculus! Before specifying a function f (:E) first determine requirements for its derivative f' (;z:) For example, one of the requirements is that f' (3) = 0 If you want to find a function g(z) such that g(9) =0 and g(8) = 0, then you could try g(z) =(z+9)(z8) If you have a possible function for f' (:c) then use the technigues in Indefinite Integrals this Module to try a possible f(z). You can generate a plat of your function by clicking the plotting option (the page option with a "P" next to your function input). You may want to do this before clicking "How Did | Do?" Notice that the label " f (:r:) ="1Is already provided for you Once you are ready to check your function, click "How Did | Do?" below (unlimited attempts) Please note that the bounds on the z-axis go from -6 to 6 It is recommended that you put a multiplication symbaol between variables or between a variable and (should you use it). Example: Write sin (7 - z)instead of sin (mz). flz)= ab sin (a) oo a i o x4 3 x3 9x 4+ 4 2 2 &amp