m408k_test3_review

m408k_test3_review - Test 3 review Drawing the graph of a...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Test 3 - review Drawing the graph of a function. Determine the intervals where f increases ( f 0 > 0), decreases ( f 0 < 0), is concave up ( f 00 > 0), is concave down ( f 00 < 0). Horizontal asymptotes: find lim x →∞ f ( x ) and lim x →-∞ f ( x ). Vertical asymptotes: find points c where lim x c - f ( x ) = ±∞ or lim x c + f ( x ) = ±∞ . Optimization problems. 1) Express the quantity that you want to optimize Q as a function of only one variable x (usually you start with a function of more variables, but there is a constraint that they satisfy such that you can express all the variables in terms of one of them). 2) Differentiate Q ( x ) and solve the equation Q 0 ( x ) = 0 for x . The absolute maximum or minimum of Q appears either there or at an end point of the domain. Antiderivatives. F ( x ) is an antiderivative of f ( x ) ⇐⇒ F 0 ( x ) = f ( x ) . Examples: sketch the graph of antiderivatives, find a particular antiderivative of a function (determine the constant such that some condition is satisfied). Inverse function.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/11/2009 for the course CH 54695 taught by Professor Lyon during the Fall '07 term at University of Texas.

Page1 / 3

m408k_test3_review - Test 3 review Drawing the graph of a...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online