Let f(x) = x2+x+ be a quadratic function with ,, R. Consider the closed interval [a, b] which has midpoint c = a+b . Prove that the slope of the secant line join- 2 ing (a, f (a)) to (b, f (b)) is equal to the slope of the tangent line to f (x) at the point c. b. What you did in part a. was prove that the midpoint c is the same as the point c specified in the Mean Value Theorem applied to f(x) on the interval [a,b]. This is a special property of quadratic functions. It does not work in general. Find a counter example to demonstrate this. Your counterexample should specify both the function and the interval you are looking at.

a. Let f (3:) = 0:332 +633+7 be a quadratic function with a, ,8, 'y 6 IR. Consider the closed interval [(1, b] which has midpoint c = \"2;? Prove that the slope of the secant line join- ing (a, f(a)) to (b, f(b)) is equal to the slope of the tangent line to f(a:) at the point c. b. What you did in part a. was prove that the midpoint c is the same as the point c specied in the Mean Value Theorem applied to f (cc) on the interval [(1, b]. This is a special property of quadratic functions. It does not work in general. Find a counter example to demonstrate this. Your counterexample should specify both the function and the interval you are looking at