math notes for test 2

math notes for test 2 - Sec 3.5 – The Chain Rule Sec 3.6...

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Topics for Test #2 Math 141- Spring 2008 Definition of the derivative – review 2.2 – limit def’n on derivative Sec.2.6 Tangents, Velocities and other rates of change Sec. 2.7 – Derivative is the instantaneous rate of change Knowing the difference between instantaneous rate of change at a point and the average rate of change over an interval. Sec. 2.8 – The derivative as a function Notations for the derivative Theorem 4 p.161 about continuity and differentiability Higher-order derivatives21 Sec. 2.9 – What does the derivative say about the function? Concavity Sec. 3.1-Derivative of Polynomials and Exponential functions Power Rule Constant multiple rule Derivative of sums and differences of functions Derivative of exponential functions Sec. 3.2 – The Product and Quotient Rules p. 198 has a table summarizing 3.1 and 3.2 rules boxed in red Sec. 3.4 – Derivative of Trigonometric Functions
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Unformatted text preview: Sec. 3.5 – The Chain Rule Sec. 3.6 – Implicit Differentiation Derivative of inverse sine function and inverse tangent function Sec. 3.7 – Derivative of Logarithmic Functions Method of logarithmic differentiation Sec. 3.8 – Linear Approximation and Differentials L ( x ) = f ( a ) + ′ f ( a )( x-a ) The linearization of f at x=a is the tangent line to the curve f(x) at x = a. It is the best straight line approximation to the curve f(x) at x=a. The closer the x-values are to a, the better the straight line approximates the function. dy =′ f ( x ) dx dy is the “differential” ; it is the change in y-values along the tangent line give a certain change in the x-values. dy approximate ∆ y ; ∆ y is the actual change in y-values along the function given a certain change in the x-values....
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This note was uploaded on 04/03/2008 for the course MA 141 taught by Professor Wears during the Spring '07 term at N.C. State.

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math notes for test 2 - Sec 3.5 – The Chain Rule Sec 3.6...

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