Code this in Python
2. Consider the curve given by +2r3y=8 (a) Find b Find the points (x and y coordinates where the graph of the equation has a horizontal tangent line.
c Find the points (r and y coordinates where the graph of the equation has a vertical tangent line.
d Plot the curve (using plot implicit and the tangent lines from parts (b and c
3. A bacteria culture grows at a rate proportional to its size. After 2 hours, the bacteria count was 1000 and after 6 hours, the bacteria count was 40,000. a Solve a system of equations to find k and yo for y-oc Note it will help to assume k is real in the symbols command.) (b) Use this to determine when the bacteria count reaches 2,000,000 c Suppose 1000 was the initial amount and 40,000 was the count after 4 hours. Find and the amount of bacteria 2 hours BEFORE the initial time. In a print statement explain what you notice when comparing these answers to part a.