5. Which of the following is equal to the slope of the tangent line? A. Average rate of change C. Slope of the secant line B. Instantaneous rate of change D. Slope of the line perpendicular to the given tangent line 6. Find lim 2hx + h2 A. 2x B. 2x +h C. 2 + h D. 2h h-+0 h 7. Find lim C. -2 h-1 2h -3' A. 4 B. 2 D. -4 8. If f (x) = 2x - 1, what is f(x + h) - f(x)? A. 2x + 2h - 1 B. 2h C. 2h - 1 D. 2h - 2 For numbers 9 and 10: Tangent and normal lines are drawn to the curvey = x' at x = 2. 9. What is the equation of the line tangent to the curve at the given point? A. y = 12x - 16 B. y = x - 12 C.y = x - 16 D. y = 12x 10. What is the equation of the normal line drawn to the curve at the given point? A. y = : x +8 B. y = x + 98 C. y = * + 49 12 6 D. y = x +9 11. Determine the derivative of f(x) = x2 - 2x + 1. A. 2x - 2 B. 2x + 2 C. 2x D. 2 12. What is the slope of the line tangent to the function in no. 11 at x = 1? A. 0 B. 2 C. 4 D. 5 13. Given f(x) = 2x + 4, what is the value of f'(1)? A. 6 B. 1 C. 4 D. 2 14. What is the derivative of f(x) = x + 5? A. 4 B. 1 C. 5 D. O 10. Find f'(x) if f(x) = x2+ 2x - 5. A. 2x B. 2x + 2 C. 2x +3 D. 2x - 5 Reflection: Guide questions: 1. How do you find the activities given? 2. What are your learnings and difficulties in this lesson? 3. How are you going to address these difficulties? Adapted and modified from the SLM of Department of Education - Region IIITo assess your understanding of the indicated learning competencies, perform this learning task. Direction: Use separate sheet of paper for your answers and solutions. Activity 1: Where's My tangent Line? Illustrate the line tangent to the following curves at the given points. 2. 3-5. Activity 2: What's the equation of tangent line? Find the equation of the tangent line to the following functions at the specified points if it exists. Show complete solution. Formula: a. mtan = lim [(2)-f(x1) X-x1 x - x1 b. y - y1 = m(x - x1) 6. f(x) = x2 + 1 at the point (0,1) 7. f(x) = x2 - 2x + 1 at the point (2,1) Activity 3: Find My Derivative. Find f'(x) using the definition of the derivative. Show complete solutions. Formula: f (x) = lim [(+h) -f(x) h-0 h 8. f(x) = 6x +4 9. f(x) = x2 - 4x +1 Analysis: Express what you have learned in this lesson/activities by answering the questions below. 1. Do all curves have a slope? Explain 2. How do you think will the tangent line be drawn at the maximum point? At the minimum point? 3. How can you relate the derivative of a function to the slope of the tangent line? Assessment: Multiple Choice. Read and analyze each question. If answer is not among the choices, write the correct one. 1. Which of the following does NOT define the slope of the tangent line to the curve? A. It is constant. B. It is not constant and must be determined by a point. C. It is equal the derivative of the function. D. It is derived from the concept of the slope of a second line. 2. On which of the following conditions will a tangent line exist? A. Function continuous at P. B. Function discontinuous at P. C. Curve with cusp at P. D. Curve with corner at P. 3. Which of the following describes a line tangent to a given curve drawn at its maximum or minimum point? A. has a positive slope B. horizontal C. has a negative slope D. vertical 4. Which is the line perpendicular to the tangent line at the point of tangency? A. secant B. parallel C. skew D. normal