Can you please help me with the following problems that are circled. That being 41, 69, 1, and 20. Thanks so much! :)

67. Which values of c satisfy the conclusion of the MVT on :he interval [0.1;] iff is a linear function? 63. Show that if f is any quadratic polynomial, then the midpoint c : b a + satises the conclusion of the MVT on [51, b] for any a and b. @Supposc that fit?!) = 2 and f'(x) 5 3 for x > 0. Apply the MVT [h e interval [0,4] to prove that f [4) 5 14. Prove more generally that x) 5 2+3x forallx :- 0. 70. Show that ifZ} = 2 and f"(x) 2 5 forx :- 2, then f(4) 3 8. 71. Show that if f(2)=5 and for] 2 10 for x > 2, then x)? 10x 15 for all x :> 2. 78. Q Dene f(x) = x3 sin (3 forx 9e 0 and f(0) = 0. (a) Show that f" is continuous at I = 0 and that x = 0 is a critical point of f. (b) @ Examine the graphs of f and J\". Can the First Derivative Test be applied