Thông tin tài liệu
Differentiation (2) Formulas Rules for differentiation The product rule: The quotient rule: The chain rule: Equation of tangent Stationary points: stationary points of a function are the points where (differentiate ; find so that ; draw sign diagram) Local maximum: Local minimum: Stationary inflection Inflection points: (differentiate ; find Stationary inflection: Non-stationary inflection: Example (Mock SAT 2): Exercise Find the derivative a) so that ; draw sign diagram) b) c) d) Exercise We have, a) Find the y-intercept of the tangent to at the point (i) We have, Equation of tangent: => y-intercept: (ii) We have, Equation of tangent: y-intercept: (iii) We have, Equation of tangent: y-intercept: b) Make the conjecture about the y-intercept of the tangent at , y-intercept: c) Prove the conjecture Equation of tangent: y-intercept: Exercise Given a) Find f’(x) b) Find f’’(x) c) Find the x-coordinates of all inflection points => or =>=> changes sign at and d) Determine whether or not these inflection points are stationary inflection points ● ● => => stationary inflection => => non-stationary inflection Exercise Consider the function of a) Show that has a local maximum at Sign diagram + - has a local maximum at b) Determine the coordinates of the inflection point of Sign diagram - + has an inflection point at c) On the graph above, draw a tangent that há a greater y-intercept than that of the tangent shown d) Show that the tangent to tangent to the graph of at the point where has the equation of tangent => => Equation of tangent => => => e) Using the equation given in part (d) , determine the value of that maximizes the y-intercept of tangent to the graph of at the point where y-intercept: or Sign diagram 0 + - y-intercept max when Exercise The population of Devils: ( is the time in years) a) Find and show that the population of Devils is always increasing b) Find and interpret the meaning of Rate of change = Devils’ population is increasing at the rate of 57 individuals per year after year c) Find d) Find the time when the population of Devils is increasing at the highest rate Rate of change = changes sign from + to - at The population of Devils is increasing at the highest rate when year e) Find the time when the population of Devils is increasing at the rate of 30 individuals per year
Ngày đăng: 03/10/2021, 23:21
Xem thêm:
