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[DOC File]Extrema and the Mean Value Theorem
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Proof: Consider the graph of and secant line as indicated in the figure. By the Point-Slope form of line we have . ... Use the First Derivative Test to find the intervals where the function increases and/or decreases . Identify all absolute and relative max and mins. Sketch the graph.
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[DOC File]Chapter 3
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Slope of the secant line though curve f on [a, b] Standard: Alternate: Instantaneous rate of change of f at . Slope of the line tangent to the curve of f at . Derivative of f at . Standard: Alternate: 1. Consider the function where. a. Find the average rate of change in f on the interval [-1, 2] b. Using the standard definition of a derivative ...
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[DOC File]Section 1
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Higher order Derivative – taking the derivative of a function a second or more times. Key Concept: There are many uses and notations for higher order derivatives: First derivative: Second derivative: Third derivative: Fourth derivative: Nth derivative: Practice: 1. Find for y = 5x³ + 4x² + 6x + 3 . 2. Find . 3. Find where . 4.
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[DOC File]Section 1
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(Euclid) Given a secant line of a curve, as Q → P , the secant line approaches the tangent line at P, i.e., the tangent line is the limiting position. If P has coordinates (a, f(a)) and Q has coordinates (a + h, f(a+h)), then. and Example 1: Find the slope of the tangent line to the curve f(x) = 3 - 2x – 2x2 where x = 1.
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[DOC File]Inverse Functions
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The Derivative Formulas of the Inverse Trigonometric Functions. If is a differentiable function of then the generalized derivative formulas for the inverse trigonometric functions are (we introduce them here without a proof): Example 3: Differentiate . Solution: Let so . Example 4: Differentiate . Solution: Let so . Example 5: Find if ...
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[DOC File]Calculus 1 Lecture Notes, Section 2.9
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Proof: Case #1: f(x) is constant on [a, b]. Then f ( (c) = 0, because the derivative of a constant is zero. Case #2: f(x) is not constant on [a, b]. It must be the case then that f(x) increases to the right of a, or that f(x) decreases to the right of a. ... where is the equation of the secant …
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[DOCX File]Transformations and Definitions
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If a secant and a tangent intersect in the exterior of a circle, then the product of the lengths of the secant segment and its external segment equals the length of the tangent segment squared (Holt) write equation the equation of a circle described algebraically or geometrically (G.GPE.1; G.4.D)
sechx

[DOC File]Calculus 1 Lecture Notes, Section 2.3
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This slope is found by taking the limit of the slopes of secant lines that get closer and closer to the point in question. (Sections 2.1 and 2.2) ... Proof: Let k(x) = f(x) - g(x). The derivative of the product of a function and a constant is the product of the constant and the derivative of the function: Proof: Let k(x) = …
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[DOC File]Calculus C
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Definition of a Derivative: The derivative of a function at a number , denoted by , is given by . Clearly explain the definition of a derivative (as stated above). Be sure include the meaning of , and “limit” in your explanation. Explain how this definition of a derivative relates to secant and tangent lines.
derivative of secant x

Derivative of secant proof