Solve all the problems 1. Solve the following equations. 15 points () 3*+2 71-a (b) In (3x) = In (4x + 1) + In (1 x) 2. Use the limit definition to find to find the derivative of the following functions. 20 points (a) f(x) x3 + x (b) f(x) = x2 +x +2 3. Find the derivative of the following functions. 30 points () (x3 + x)2 (d) y = 3-2 7x+1 (x + 2x + 2)(x3 + 3x + 3) ez+2 ln(2x + 10) (b) y = 1+ x + x + x6 +x7 (e) y = (c) y 2x-7 (f) y = 4. Find the Maximum or Minimum values of the following function. 20 points f (x) = x3 + 3x 9 + 4 5. As the operator of Workout Fever Health Club, you calculate your demand equation to be q = -0.06p + 84 15 points where is the number of members in the club and p is the annual membership fee you charge. (a) Your annual operating costs are a fixed cost of $20, 000 per year plus a variable cost of $20 per member. Find the annual revenue and profit as functions of the membership price p. (b) At what price should you set the annual membership fee to obtain maximum revenue? What is the maximum possible revenue? (c) At what price should you set the annual membership fee to obtain maximum profit? What is the maximum possible profit? Formulas: ()' = f, (fg)' = f'g+ fg', f'(x) = lim,-0 f(x+h)-f(x) (x")' = nx"-1