Page Description Equation
227 absolute (global) maximum value \[ \]
227 absolute (global) minimum value \[ \]
227 absolute (global) extrema (extremum) \[ \]
228 Extreme-Value Theorem for Continuous Functions \[ \]
229 local (relative) maximum value \[ \]
229 local (relative) minimum value \[ \]
230 local (relative) extrema \[ \]
230 Theorem 2 Local Extreme Values \[ \]
230 critical point \[ \]
237 Rolle’s Theorem \[ \]
238 Mean Value Theorem \[ \]
240 Corollary 1. Functions with Zero Derivatives \[ \]
240 Corollary 2. Functions with Same Derivatives \[ \]
241 differential equation (definition) \[ \]
241 solution to differential equation (definition) \[ \]
241 projectile motion \[ \]
241 free-fall \[ \]
242 projectile motion \[ \]
246 increasing function \[ \]
246 decreasing function \[ \]
246 Corollary 3. First Derivative Test for Increasing/Decreasing \[ \]
247 First Derivative Test for Local Extrema \[ \]
248 concave up \[ \]
248 concave down \[ \]
249 Second Derivative Test for Concavity \[ \]
249 inflection point \[ \]
250 stock market and inflection points \[ \]
251 Second Derivative Test for Local Extrema \[ \]
252 how to graph $y=f(x)$ using $y'$ and $y''$ \[ \]
253 possible graphs described by $y'$ and $y''$ \[ \]
258 autonomous differential equation \[ \]
258 equilibrium value (rest point) \[ \]
258 phase line \[ \]
258 how to draw phase lines and solution curves \[ \]
259 stable equilibrium \[ \]
260 unstable equilibrium \[ \]
261 Newton’s Law of Cooling \[ \]
261 falling body with resistive forces \[ \]
262 terminal velocity \[ \]
263 limiting population (carrying capacity) \[ \]
263 logistic growth \[ \]
263 sigmoid shape \[ \]
267 optimization \[ \]
269 How to solve min-max problems \[ \]
272 Snell’s Law \[ \]
272 economics \[ \]
272 marginal revenue \[ \]
272 marginal cost \[ \]
272 marginal profit \[ \]
273 Theorem 6. Maximum Profit At a production level yielding maximum profit, marginal revenue equals marginal cost. \[ \]
274 average daily cost \[ \]
275 sensitivity of minimum cost \[ \]
285 linearization \[ \]
285 standard linear approximation \[ \]
285 center of the approximation \[ \]
286 linear approximation for roots and powers \[ \]
287 common linear approximations \[ \]
287 differentials \[ \]
289 differential estimate of change \[ \]
289 absolute change \[ \]
289 relative change \[ \]
289 percent change \[ \]
291 sensitivity to change (using differentials) \[ \]
291 error in measurement (using differentials) \[ \]
292 error in differential approximation \[ \]
292 energy and Einstein’s mass equation \[ \]
298 Newton’s method for solving equations \[ \]
300 convergence is usually assured (Newton’s method) \[ \]
301 If Newton’s method converges it converges to a root. \[ \]
301 When Newton’s method converges to a root, it might not be the one you have in mind. \[ \]
302 fractal basin \[ \]
311 Schwarz’s inequality \[ \]
311 estimating reciprocals without division \[ \]