5.1.2 	The derivative and mean value theorems

Factoring Functions, J. C. Bodenrader, 2:1, 1971, 23-26, 0.6, 3.2, 9.1
How Steep Is a Hill?, Robert L. Page, 3:1, 1972, 66-67, C
A Note on Derivatives of Polynomials, Aron Pinker, 3:2, 1972, 77-78, C
Generalizing Rolle's Theorem in Elementary Calculus, Rodney D. Gentry, 4:3, 1973, 11-17
Calculus by Mistake, Louise S. Grinstein, 5:4, 1974, 49-53, C, 5.1.4, 5.2.2, 5.2.3, 5.2.5, 5.2.3, 5.7.2, 5.2.10, 5.4.2, 5.6.1
Continuous Deformation of a Polynomial into Its Derivatives, Roland E. Larson, 5:2, 1974, 68-69, C, 0.7
When Does (fg )'=f'g'?, Lewis G. Maharam and Edward P. Shaughnessy, 7:1, 1976, 38-39, C
Comparing a^b and b^a Using Elementary Calculus, John T. Varner III, 7:4, 1976, 46, C, 5.1.1
An Elementary Result on Derivatives, David A. Birnbaum and Northrup Fowler III, 8:1, 1977, 10-11
Some Elementary Results Related to the Mean Value Theorem, Roy E. Myers, 8:1, 1977, 51-53, C
Differentiating Area and Volume, Jay I. Miller, 9:1, 1978, 47-49, C
Some Functional Equations for the Calculus Student, Stephen J. Milles and Henry J. Schultz, 9:4, 1978, 205-209
Differentiation and Synthetic Division, Dan Kalman, 10:1, 1979, 37, C
Travelers' Surprises, R. P. Boas, 10:2, 1979, 82-88
Another Application of the Mean Value Theorem, Norman Schaumberger, 10:2, 1979, 114-115, C
An Alternate Approach to the Derivative of the Trigonometric Functions, Norman Schaumberger, 10:4, 1979, 276-277, C
Derivatives Without Limits, Harry Sedinger, 11:1, 1980, 54-55, C, 5.1.3
Wavefronts, Box Diagrams, and the Product Rule: A Discovery Approach, John W. Dawson, Jr., 11:2, 1980, 102-106, 7.2
A Geometric Proof of Cauchy's Generalized Law of the Mean, Mary Powderly, 11:5, 1980, 329-330, C
A Mean Generating Function, Jack C. Slay and J. L. Solomon, 12:1, 1981, 27-29, 7.3
Who Needs Those Mean-Value Theorems, Anyway?, Ralph Boas, 12:3, 1981, 178-191
The Sums of Zeros of Polynomial Derivatives, Michael W. Ecker, 13:5, 1982, 328-329, C
Exactly n-Times Differentiable Functions, Robert Bumcrot, 14:3, 1983, 258-259, C
The Derivatives of Sin x and Cos x, Norman Schaumberger, 15:2, 1984, 143-145, C
Another Look at x^(1/x), Norman Schaumberger, 15:3, 1984, 249-250, C, 5.4.1
Alternate Approaches to Two Familiar Results, Norman Schaumberger, 15:5, 1984, 422-423, C, 5.1.1
A Self-Contained Derivation of the Formula of the Derivative with Respect to x of x^r for Rational r, Peter A. Lindstrom, 16:2, 1985, 131-132, C
Average Values and Linear Functions, David E. Dobbs, 16:2, 1985, 132-135, 5.2.1
Testing Understanding and Understanding Testing, Jean Pedersen and Peter Ross, 16:3, 1985, 178-185, 0.2, 1.2, 5.2.2
More Applications of the Mean Value Teorem, Norman Schaumberger, 16:5, 1985, 397-398, C
Rolle over LagrangeÑAnother Shot at the Mean Value Theorem, Robert S. Smith, 17:5, 1986, 403-406
A Guide to Computer Algebra Systems, John M. Hosack, 17:5, 1986, 434-441, 0.4, 4.1, 5.1.5, 5.2.3, 5.2.4, 5.2.5
The Derivatives of the Sine and Cosine Functions, Barry A. Cipra, 18:2, 1987, 139-140, C, 5.2.1
A General Form of the Arithmetic-Geometric Mean Inequality via the Mean Value Theorem, Norman Schaumberger, 19:2, 1988, 172-173, C, 9.5
A Direct Proof of the Integral Formula for Arctangent, Arnold J. Insel, 20:3, 1989, 235-237, C, 5.2.6, 5.2.3
Automatic Differentiation and APL, Richard D. Neidinger, 20:3, 1989, 238-251, 5.1.3
The Power Rule and the Binomial Formula, Stephen H. Friedberg, 20:4, 1989, 322, C, 5.4.2
A Simple Auxiliary Function for the Mean Value Theorem, Herb Silverman, 20:4, 1989, 323, C
The Function sin x / x, William B. Gearhart and Harris S. Shultz, 21:2, 1990, 90-99, 2.2, 5.1.5
FFF #26. Differentiating the Square of x, Ed Barbeau, 21:4, 1990, 304, F
The Derivative of x^n = nx^(n-1): Six Proofs, Russell Jay Hendel, 21:4, 1990, 312-313, C
FFF #37. 3 Equals 2, Ed Barbeau, 22:2, 1991, 132, F
The Differentiability of Sin x, David A. Rose, 22:2, 1991, 139-142, C
FFF #45. All Powers of x are Constant, Ed Barbeau, 22:5, 1991, 403, F, 0.9
FFF #47. A Natural Way to Differentiate an Exponential, Ed Barbeau, 22:5, 1991, 404, F, 5.1.3 (also 23:3, 1992, 206 and 24:3, 1993, 231)
Summation by Parts, Gregory Fredricks and Roger B. Nelsen, 23:1, 1992, 39-42, C, 5.4.1, 5.4.2, 9.3
FFF #56. Yet Another Proof that 3 Equals 2, Ed Barbeau, 23:3, 1992, 204, F (also 23:4, 1992, 306)
Another Proof of the Formula e equals the infinite sum of reciprocals of n!, Norman Schaumberger, 25:1, 1994, 38-39, C, 5.3.2
Why Polynomials Have Roots, Javier Gomez-Calderon and David M. Wells, 27:2, 1996, 90-94, 5.7.1, 9.5
Newton's Method for Resolving Affected Equations, Chris Christensen, 27:5, 1996, 330-340, 0.7, 5.4.3
FFF #132. The Increment of a Product, Robert Weinstock, 29:4, 1998, 302-303, F
On ÒRethinking Rigor in Calculus É,Ó or Why We DonÕt Do Calculus on the Rational Numbers, Scott E. Brodie, 30:2, 1999, 135-138, C, 1.2
FFF #142.  Calculating the Average Speed, Bill Simpson, 30:3, 1999, 209, F, 6.1
A Natural Proof of the Chain Rule, Stephen Kenton, 30:3, 1999, 216-218, C
Things I Have Learned at the AP Reading, Dan Kennedy, 30:5, 1999, 346-355, 0.2, 5.1.1, 5.2.1, 5.2.6, 5.4.2, 6.1
From Square Roots to n-th Roots: NewtonÕs Method in Disguise, W. M. Priestley, 30:5, 1999, 387-388, C, 9.6
Amortization: An Applications of Calculus, Richard E. Klima and Robert G. Donnelly, 30:5, 1999, 388-391, C, 0.8
Can We Improve the Teaching of Calculus?, Hugh Thurston, 31:4, 2000, 262-267, 1.1, 5.7.1
Meta-Problems in Mathematics, Al Cuoco, 31:5, 2000, 373-378, 0.7, 9.3
FFF #174. A Strong Differentiability Conclusion, Sarah V. Cook, 32:4, 2001, 281-282, F
Hat Derivatives, Stephen B. Maurer, 33:1, 2002, 32-37, 5.3.2
On a Mean Value Theorem, Peter R. Mercer, 33:1, 2002, 46-48, C
The Mean Value Theorem for Parabolas (Mathematics Without Words), Lance E. Hemlow, 33:2, 2002, 136, C
Adding Fractions, Dan Kalman, 34:1, 2003, 41, C, 0.1
Higher Derivatives and Economics, Charlie Marion, 37:2, 2006, 124, C
Controlling the discrepancy in marginal analysis calculations, Michael W. Ecker, 37:4, 2006, 299-300, C