Calculus: Analytic Geometry and Calculus, with Vectors

286 Functions, graphs, and numbers for which xo - S < x < xo + S lies entirely on or above L or lies entirely on or below ...

5.1 Graphs, slopes, and tangents 287 mathematics before we can fully comprehend the details. In the worst of circumstances, we a ...

288 Functions, graphs, and numbers 5.27, which we do not bother to read now, proves that this idea is correct and that a < b. ...

5.1 Graphs, slopes, and tangents 289 whenever 111 < 82. This gives (5.171) and completes the proof of Theorem 5.17. As was re ...

290 Functions, graphs, and numbers the unqualified assertion that one of r and p is a differentiable function of the other is qu ...

5.1 Graphs, slopes, and tangents 291 prove that the graph has exactly one tangent at Po and that the equation of this tangent is ...

(^292) Functions, graphs, and numbers say something very specific about the slopes of graphs of y = sin x and y = cos X. Sketch ...

S.1 Graphs, slopes, and tangents 293 19 It is easy to show that the graph of the equation (1) x4 + 2x2y2 + y4 - 2x3 - 2x2y - 2xy ...

294 Functions, graphs, and numbers has a tangent at each point where it does not have a corner. We can wonder whether we can ass ...

5.2 Trends, maxima, and minima 295 Definition 5.24 Let f be defined over a nonempty set S in El. We say that f has a local (or r ...

296 Functions, graphs, and numbers put plus signs above intervals over which f'(x) > 0 and the graph of f has positive slope, ...

5.2 Trends, maxima, and minima 297 that f has an extremum at xo. It does imply that if f hasan extremum at xo, then xo must be e ...

298 Functions, graphs, and numbers 2 Letting f(x) = axe + bx + c where a > 0,ll show that f (x) = 2a (x -{ 2a). Tell why f is ...

5.2 Trends, maxima, and minima 299 Our first step is to draw Figure 5.291 and look at it.^24 Our good sense should tell us that ...

300 Functions, graphs, and numbers 15 Show that of all rectangles having a given area, a square has the least perimeter. 16 Find ...

5.2 Trends, maxima, and minima 301 hours per week. Find the number of secretaries that will turnout the most work. Discussion an ...

302 Functions, graphs, and numbers feet if r > s and this number is positive. Investigation of the whole matter is not as sim ...

5.2 Trends, maxima, and minima 303 Prove that L is maximum when an appropriate angle 0 satisfies the equation cot 0 = 0. 33 A sp ...

(^304) Functions, graphs, and numbers use the result to determine the population of a Utopian country that minimizes the burdens ...

5.3 Second derivatives, convexity, and flexpoints 305 The information contained in these theorems is sometimesvery helpful when ...