Please answer the following NEATLY make sure you have full solutions and answer CORRECTLY

5. Using the graph of the function f(x) = x3 - x + 1 i. Find approximate x values for any local maximum or local minimum points. ii. Set up a table showing intervals of increase or decrease and the slope of the tangent on those intervals. iii. Set up a table of values showing "x" and its corresponding "slope of tangent" for at least 7 points iv. Sketch the graph of the derivative using the table of values from (iii) 6. Find the derivative of the following functions using the lim f(xth)-f(x) definition of the derivative. h-0 h a. f (x) =5x3 b. f ( x) = 27 : Show all your steps. 7. A rocket is fired into the air with an initial velocity of 98 m/s. The height (h ) of the rocket after t seconds is given by the expression h = 98t - 4.91-. a. What the average rate of change over the first 2 seconds. b. At what point does the rocket reach its maximum height? Show a graphical and algebraic solution. c. Over what intervals is the rocket's height increasing and decreasing