185 74. Show that 5 is a critical number of the function g(x) = 2 + (x-5) but g does not have a local extreme value at 5. 319 447 742 1325 1445 75. Prove that the function 4151 the cubic e shuttle for polynomial. e and use it es of the dpipe) pward caus- ccompanied er channel mount of 51 f(x) = x10 + x + x + 1-6) as has neither a local maximum nor a local minimum. 76. If f has a local minimum value at c, show that the function g(x) = f(x) has a local maximum value at c. AP-CS 77. Prove Fermat's Theorem for the case in which f has a local minimum at c. 78. A cubic function is a polynomial of degree 3; that is, it has the form f(x) = ax + bx + cx + d, where a 0. 3 2 (a) Show that a cubic function can have two, one, or no criti- cal number(s). Give examples and sketches to illustrate the three possibilities. (b) How many local extreme values can a cubic function have? niz + 6200 S = (0) !