Calculus – Application of Derivatives ii
Book Calculus by Thomas/Finney, 9th Edition, Page 205 Function’s critical points, local extreme values. How to test for local extreme values. At left and right endpoints? Graphing
Calculus
Calculus – Application of Derivatives
Book calculus by Thomas/Finney, 9th Edition, Page 189 Derivatives can be used to analyze the behaviour of functions and solve practical optimization problems. Max-Min Theorem relates to existence of max and min value for a function $f4$ that is continous at every point of closed interval I. Absoluted maxima and minima on a closed interval ... Read More
Calculus – Derivatives
Book Calculus by Thomas/Finney, 9th Edition, Page 109 Derivates is one of the most important concept in calculus. It measures the rate at which a function changes. It is defined actually as the limit of secant slopes which is the slope of curve at a point. Derivative of the funtion $f$ with respect to variable ... Read More
Calculus – Limits and Continuity
Book Calculus by Thomas/Finney, 9th Edition; Page 51 Limit: One of the main concept that differentiates calculus with algebra and trigonometry (page 51). Core concepts: limit, limits to describe how different functions changes or varies (continuously or erratically), how limits can be used to define tangent lines to the graph of the functions, derivative of ... Read More
Calculus – Trignometric Functions
Book: Calculus by Thomas/Finney. 9th Edition Radian is a unit of measurment. In calculus, angle is measured in radian. (Navigation and astronomy uses degrees for angles) – page 35 Radian measure $\theta$ is given by $\frac{s}{r}$ wher $s$ is arc length AB and $r$ is the radius. Six basic trigonometric functions. Some other functions. For ... Read More
Calculus – Rate of Change and Limit
Finney, R. L., Giordano, F. R., Weir, M. D., Thomas, G. B., Jr., & Calculus and analytic geometry. (2001). Thomas’ calculus (Tenth edition / based on the original work by George B. Thomas, Jr.,as revised by Ross L. Finney, Maurice D. Weir, and Frank R. Giordano.). Addison-Wesley. Average rate of change of function $y=f(x)$ is given by ... Read More
Calculus – Functions
Finney, R. L., Giordano, F. R., Weir, M. D., Thomas, G. B., Jr., & Calculus and analytic geometry. (2001). Thomas’ calculus (Tenth edition / based on the original work by George B. Thomas, Jr.,as revised by Ross L. Finney, Maurice D. Weir, and Frank R. Giordano.). Addison-Wesley. y is called the function of x if, $y = ... Read More
Calculus – Coordinates, Lines and Increments
Finney, R. L., Giordano, F. R., Weir, M. D., Thomas, G. B., Jr., & Calculus and analytic geometry. (2001). Thomas’ calculus (Tenth edition / based on the original work by George B. Thomas, Jr.,as revised by Ross L. Finney, Maurice D. Weir, and Frank R. Giordano.). Addison-Wesley. The coodinates of point $P(a,b)$ are $a$ and $b$. $a$ ... Read More
Calculus – Preliminaries
Finney, R. L., Giordano, F. R., Weir, M. D., Thomas, G. B., Jr., & Calculus and analytic geometry. (2001). Thomas’ calculus (Tenth edition / based on the original work by George B. Thomas, Jr.,as revised by Ross L. Finney, Maurice D. Weir, and Frank R. Giordano.). Addison-Wesley.
Calculus – The Derivative
Suppose function $latex y = f(x)$, then the derivative of the function can be denoted as: $latex f'(x), \frac{dy}{dx}, y’ or \frac{d}{dx}(f(x))$ BUT what does that mean actually? Derivative of a function? https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/03%3A_Derivatives/3.02%3A_The_Derivative_as_a_Function