The document provides instructions for a basic calculus performance task involving differentiation rules and optimization problems. Students are asked to solve 14 problems applying differentiation rules to find derivatives of various functions. They are also asked to solve 3 optimization problems by sketching, identifying variables, taking derivatives to find critical points, and determining maximum or minimum values. The tasks are assessed based on accuracy of computations, conceptual understanding demonstrated, and inclusion of proper labels and units.
The document provides instructions for a basic calculus performance task involving differentiation rules and optimization problems. Students are asked to solve 14 problems applying differentiation rules to find derivatives of various functions. They are also asked to solve 3 optimization problems by sketching, identifying variables, taking derivatives to find critical points, and determining maximum or minimum values. The tasks are assessed based on accuracy of computations, conceptual understanding demonstrated, and inclusion of proper labels and units.
The document provides instructions for a basic calculus performance task involving differentiation rules and optimization problems. Students are asked to solve 14 problems applying differentiation rules to find derivatives of various functions. They are also asked to solve 3 optimization problems by sketching, identifying variables, taking derivatives to find critical points, and determining maximum or minimum values. The tasks are assessed based on accuracy of computations, conceptual understanding demonstrated, and inclusion of proper labels and units.
The document provides instructions for a basic calculus performance task involving differentiation rules and optimization problems. Students are asked to solve 14 problems applying differentiation rules to find derivatives of various functions. They are also asked to solve 3 optimization problems by sketching, identifying variables, taking derivatives to find critical points, and determining maximum or minimum values. The tasks are assessed based on accuracy of computations, conceptual understanding demonstrated, and inclusion of proper labels and units.
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Republic of The Philippines
Department of Education Region 1 Schools Division of Ilocos Norte BANGUI NATIONAL HIGH SCHOOL Bangui
Third and Fourth Performance Task, Quarter 3
Basic Calculus
COMPETENCIES: 1. Apply the differentiation rules in computing the derivatives of algebraic, exponential, logarithmic and trigonometric functions. STEM_BC11D-IIIf-3 2. Solve optimization problems that yield polynomial functions. Stem_BC11D- IIIf-3 3. Illustrate the chain rule of differentiation. Stem_BC11D-IIIh-2
ACTIVITY 1: DIFFERENTIATION RULES
Direction. Solve for the derivative of the following functions using the appropriate differentiation rules. Use the answer sheets given. 1. f(x) = (x2 – 3) (2x-3) 8. f(x) = sin (6x) + 5cos x + x -2
x 2−5 2. f(x) = 9. f(x) = log2(3x + 5) 3 x +2
3. y = 5sec (2x) + 5x 10. y = ln (12x)
4. y= 36x 11. f(x) = √ 4 x −2
5. f(x) = cot (5x3) 12. f(x) = (4x3 -3x + 2)3
4 x+1 6. f(x) = 13. y = 3x [sin (4x)] cos( x )
7. f(x) = e3x. e6x 14. y = (x-3)-1/2
ACTIVITY 2: OPTIMIZATION PROBLEM
Direction: Solve the following problems completely, following the indicated steps below. a. Create a sketch or illustration with given labels whenever necessary. b. List what is asked and what are the given data in the problem. c. Write down the constraint and optimization equations. d. Equate one variable in terms of the other from the constraint equation. Then replace or substitute it to the same variable on the optimization equation. e. Simplify the optimization equation then solve for its first derivative. f. Set the first derivative equation to zero and find the critical point. g. Test the critical point values using the derivative tests. h. Substitute the critical value to solve for the other.
1. From a piece of cardboard that is 24 cm by 48 cm, cut equal squares out of the corners. Fold up the sides to form an open box. Determine the height of the box that will give the maximum volume.
2. A rectangular chicken pen is bounded on one side by the wall of the house and the other three sides by 160 meters of fences. Find the dimensions of the chicken pen if the area is a maximum.
3. Find the dimensions of a rectangle of maximum area that can be inscribed in a circle of radius 4 cm.
Criteria 0 1 2 DIFFERENTIATION RULES Computation The answer and The answer is The answer and the strategies were incorrect but the strategies used to incorrect strategy used to solve solve the problem are the problem correct correct OPTIMIZATION PROBLEM 0 1 2 Conceptual a. Mathematical a. Mathematical a. Mathematical Understanding representation was representation was representation was inaccurate. inaccurate. appropriate and b. Wrong information b. Some relevant accurate. used. information was used. b. Relevant c. Procedures used c. Procedures used information was used. would not solve the would lead to a c. Procedures used problem partially correct lead to correct answer solution to the and solution problem Unit and Label The illustration and The illustration and The illustration and answer does not answer include a label answer include an include a label and and unit but it is not accurate label and unit accurate unit.
Note: Post test shall be sent through goggle forms on May 14,2021
Student Signature: ______________________________
Parent/Guradian Name & Signature: _______________________________________-
Prepared by: MARISSA G. AREOLA Subject Teacher
Checked by: GERARDO D. BALTAZAR JR. HERI BERT B. PASCUA Head Teacher III Head Teacher III
