Calculus MAT 301 Lab #3 Question | x+1, x >4 a) Explain why f'is (or is not) continuous at x = 4. b) Explain why f'is (or is not) differentiable at x =4. c) In general, what is the relationship between continuity and differentiability? Question 2 Calculate the derivative of the function f(x) = \"x; 5x + 2 and plot the function and its derivative on the same graph. Describe the relationship between the two graphs. Question 3 Let & denote the number of letters in your first name. Define the function: 1kx i a) Have Maple calculate f'(x) and f\"(x). Have Maple evaluate f3(x) and f*(x). b) Make a plot of both the function f(x) and the derivative of f(x) in the same window. Explain how the sign of the derivative is related to the graph of f(x). ) Use the solve command to find the x-coordinates of all of the points on the graph of f(x) where the derivative equals 0. Next find the y-coordinates of these points on the graph of f(x). Question 4 Plot the curve x* + * = 6xy together with the tangent to the curve at the point 4 8 (3:3)