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

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