Follow the instructions in the picture. Show all work when solving problems.

Include all of your work in solving the following questions, and be sure to follow instructions for each question. Note that if you do not justify or show work you may receive little to no credit. 1. Let F(t) denote the rise in house prices since the covid pandemic, and be given by: F(t) = 800t2 + 3000 where t = 0 denotes March 2020. Find the rate at which house prices were rising in December 2020. 1 2. Find the point on the curve y = m2 6:1: where the tangent line is perpendicular to y 3 = 5(15 + 1) 3. The position of a particle at time t in seconds is given by the function s(t) = 120 + 5t 152$2 (a) Find the average velocity of the particle between time t = 0 and t = 2. (b) Find the velocity of the particle when t = 4. 4. For the following problems, (1) you should differentiate the function with respect to the variable given (2) state the differentiation rule(s) that you used (basic rule (section 3.1), product rule, quotient rule, chain rule) Note that if you obtain a correct answer by not using the rule(s) you have stated, you may not obtain full credit. You should not simplify your answer. 1 (a) r(t) = W2 + r4 + t2 +7r (b) f (x) = (965 + (V3)? + 6)(s/5 m) 82 + 3 (0) 9(3) _ 534 + 23 (d) h(a:) = ($4 + 3;;2 + 5)9 (e) f (y) = [(y2 + 3y"')(y6 + 20" + 30)]7 i a