Updates- Go over Applications of Differentiation Test
Bell RingerWhat is the function that has a derivative of f’(x) = 2? f(x) = 2x f(x) = x2 f(x) = 2x + 1 f(x) = 2x - 3 more than one answer exists
Which of the following functions have a derivative of f’(x) = 7x and f(0) = 7 f(x) = x2 + 7 f(x) = (7/2)x2 + 8 f(x) = (7/2)x2 + 7 f(x) = -(7/2)x2 - 7 none of the above
Which of the following functions have a second derivative of f”(x) = 5 f(x) = 5x f(x) = (5/2)x2 + 4 f(x) = (5/2)x2 - 4 more than one answer exists none of the above
Solve for y: y = (-4/3)x3 + 3x + C y = (4/3)x3 + 3x + C y = (-4/3)x3 - 3x + C y = (4/3)x3 - 3x + C - none of the above
Review- Prerequisites
- Derivatives
- Derivative Rules
- Trig Derivatives
Lesson- If the derivative of a function is f'(x) = 3, what is the function?
- Antiderivative
- Indefinite Integral
- Definition
- Integral Sign
- Integrand
- Variable of Integration
- Constant of Integration
- General Solution
- Basic Integration Rules
Exit Ticket- Posted on the board at end of the block.
| Lesson Objective(s)- How can indefinite integrals be evaluated using basic integration rules?
- How are antiderivatives related to derivatives?
Standard(s) - APC.10
- Use Riemann sums and the Trapezoidal Rule to approximate definite integrals of functions represented algebraically, graphically, and by a table of values and will interpret the definite integral as the accumulated rate of change of a quantity over an interval interpreted as the change of the quantity over the interval
- Riemann sums will use left, right, and midpoint evaluation points over equal subdivisions.
- APC.11
- The student will find antiderivatives directly from derivatives of basic functions and by substitution of variables (including change of limits for definite integrals).
- APC.12
- The student will identify the properties of the definite integral. This will include additivity and linearity, the definite integral as an area, and the definite integral as a limit of a sum as well as the fundamental theorem.
- APC.13
- The student will use the Fundamental Theorem of Calculus to evaluate definite integrals, represent a particular antiderivative, and facilitate the analytical and graphical analysis of functions so defined.
- APC.14
- The student will find specific antiderivatives, using initial conditions (including applications to motion along a line). Separable differential equations will be solved and used in modeling (in particular, the equation y' = ky and exponential growth).
- APC.15
- The student will use integration techniques and appropriate integrals to model physical, biological, and economic situations. The emphasis will be on using the integral of a rate of change to give accumulated change or on using the method of setting up an approximating Riemann sum and representing its limit as a definite integral. Specific applications will include
- a) the area of a region;
- b) the volume of a solid with known cross-section;
- c) the average value of a function; and
- d) the distance traveled by a particle along a line.
Mathematical Practice(s)- #1 - Make sense of problems and persevere in solving them
- #2 - Reason abstractly and quantitatively
- #5 - Use appropriate tools strategically
- #6 - Attend to precision
- #8 - Look for and express regularity in repeated reasoning
Past Checkpoints |