PPT-Derivative of an Inverse

1980 AB Free Response 3 Continuity and Differentiability of Inverses If f is continuous in its domain then its inverse is continuous on its domain If f is increasing on its domain then its inverse is increasing on its domain . We have that AA 1 that is that the product of AA is the sum of the outer products of the columns of To see this consider that AA ij 1 pi pj because the ij element is the th row of which is the vector a a ni dotted with the th column of which is Section 3.1b. Remember, that in . graphical terms. , the derivative of a. function at a given point can be thought of as the . slope. of the curve at that point…. Therefore, we can get a good idea of what the graph of. Points of Inflection. Section 4.3a. Writing: True . or . False – A . critical point . of. a function always signifies . an . extreme. value . of the . function. Explain.. FALSE!!! – Counterexample???. Last Week Review. Matrix. Rule of addition. Rule of multiplication. Transpose. Main Diagonal. Dot Product. Block Multiplication. Matrix and Linear Equations. Basic Solution. X. 1. + X. 0. Linear Combination. Chapter 3.1. Definition of the Derivative. In the previous chapter, we defined the slope of the tangent line to a curve . at a point . as. When this limit exists, it is called the . derivative of . A bit more practice in Section 4.7b. Analysis of the Inverse Sine Function. 1. –1. D:. R:. Continuous. Increasing. Symmetry: Origin (odd . func. .). Bounded. Abs. Max. of at . x. = 1. Abs. Min. of at . FGFOA Conference, Orlando FL,. Mark A. White, CPA, Partner, Purvis Gray & Company LLP. Jim Towne, Senior VP, DerivActiv. 1. Statement 53. Accounting and Financial Reporting for Derivative Instruments. VALUE THEOREMS. Derivability of a function :. A function . f . defined on [. a, b. ] is said to be derivable or differentiable at if exists. This limit is called derivative of . -More Effort Needed!. -Wording of Problems (derivative, slope at a point, slope of tangent line…). -Product / Quotient Rules!!!. -Quiz . I:g. and . II:a. -Weekly 7 , 8 , 10 . The Chain Rule. 4.1.1. by. Dr.. . Shorouk. . Ossama. Inverse Matrix :. If . A. is a square matrix. , and if a . matrix . B. of the same size . can be found such that . AB = BA = I. , then . A. is said to be . invertible. Slope of the Tangent Line. If . f. is defined on an open interval containing . c. and the limit exists, then . . and the line through (. c. , . f. (. c. )) with slope . m. is the line tangent to the graph of . . Ossama. Inverse Matrix :. If . A. is a square matrix. , and if a . matrix . B. of the same size . can be found such that . AB = BA = I. , then . A. is said to be . invertible. and . B. is called an . The . inverse . of a relation is the set of ordered pairs obtained by . switching the input with the output. of each ordered pair in the original relation. (The domain of the original is the range of the inverse; and vice versa). Andrew Gardner, Slides 2-5, . Rafael Diaz, Slides . 9-11. Mosi. Davis. , Slides 6-8. What is the Inverse Function and how is it applied with currency?. The Inverse Function is a function used to return a value from x to y. For example: .