8. Sketch the graph of a function f(a) that satisfies all of the following conditions. f(-2) = f(2) = 2; f is increasing on (-x, -2) and decreasing on (-2,0) U (0, 0); f is concave down on (-o. 0) and concave up on (0. 0): f has a vertical asymptote : r = 0

Consider the function f(x) shown in the diagram. Draw the secant line to f(x) over the interval [0, 8] 15+ 14+ 13- 12+ 11+ 10+ 9+ 8+ 7+ 6+ 5+ -2 -1 msec 4- 3 -2 2 1 -1 + -2 -3 Clear All Draw: 15+ 14- 13+ 12 11 10+ 9+ 8+ 7+ Approximate the slope of the secant line: 6+ 5+ 4+ 3- 2+ #+ + 2 Now draw what appears to be a tangent line to f(x) at x = 6. -2 Clear All Draw: mtan~ + 2 4 Equation: || 3 3 4 6 5 7 8 9 10 11 6 Approximate the slope of the tangent line at x = 6: + + + + 7 8 9 10 11 Finally, write the equation of the line tanget to f(x) at x = 6.

13. Consider the function defined by f(x) = -x³ + 6x² - 10. (a) Determine the values of x for which f(x) is an increasing function. There is a point of inflexion, P, on the curve y = f(x). (b) Find the coordinates of P.

4. For the function x-1 8(x : x- 3 (a) Find the intervals on which the function is concave upward and the intervals on which it is concave downward. (b) Find the inflection points if any.