Let f be a differentiable function everywhere and let p be a constant. Define a function g by g(x) = px − f(x). Geometrically, g measures the vertical distances between the graph of f and the straight line, y = px. We want to understand when g has extrema, that is, the largest or smallest vertical distances between the graph of the function f and a straight line. Prove that if g has an extremum value at x = c then ƒ must have a tangent line parallel to the line y = px.

Let f be a differentiable function everywhere and let p be a constant. Define a function g by g(x) = px − f(x). Geometrically, g measures the vertical distances between the graph of f and the straight line, y = px. We want to understand when g has extrema, that is, the largest or smallest vertical distances between the graph of the function f and a straight line. Prove that if g has an extremum value at x = c then ƒ must have a tangent line parallel to the line y = px.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 36E

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