4. a. Let f(x) = ax²+3x+y be a quadratic function with a, 3, 7 € R. Consider the closed interval [a, b] which has midpoint c = ab. 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(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.

4. a. Let f(x) = ax²+3x+y be a quadratic function with a, 3, 7 € R. Consider the closed interval [a, b] which has midpoint c = ab. 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(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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 93E

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