please help me answer them

SUBJECT: BASIC CALCULUS

LESSON: SLOPE OF THE TANGENT LINE TO A CURVE

ACTIVITY 1:

What's More A. Illustrate the line tangent to the following curves at the given points. Write your answers on a separate sheet of paper. 1 . 2. 3-5. B. Find f'(x) using the definition of the derivative. Write your answers on a separate sheet of paper. 1. f(x) = 6x +4 2. f(x) = x2 -4x + 1 3. f(x) = 3x2 +8 4. f (x) = 5. f(x) = x3 -1 C. Find the equation of the tangent line to the following functions at the specified points if it exists. Write your answers on a separate sheet of paper. 1. f(x) = 3x2 - 12x + 1 at the point (0, 1) 2. f(x) = x2 + 1 at the point (0, 1) 3. f(x) = x2 - 2x + 1 at the point (2, 1) 4. f(x) = x3 + 2x - 1 at the point (0, -1) 5. f(x) = = at the point (1,1)Assessment A. Read and answer each question. 1Write your answer on a separate sheet of paper. 1. 1Which of the following does NOT dene 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. 1Which of the following describes a line tangent to a given curve drawn at its maximum or minimum point? A. has a positive slope C. horizontal B. has a negative slope D. vertical 4. Which is the line perpendicular to the tangent line at the point of tangency? A. secant C. parallel B. skew D. normal 5. 1Which of the following is equal to the slope of the tangent line? A. Average rate of change E. Instantaneous rate of change C. Slope of the aecant line D. Slope of the line perpendicular to the given tangent line. B. Evaluate {TE} for the given functions. .f{x}=5r1 Pl. 1 B 5 C.-1 D 2 7' f{xJ=3I2 A. 3 B- 2 C. 6 D. 12 8. f(x) = x2 - 6x +9 A. - 2 B. - 6 C. 1 D. 2 9. f (x) = x3 - 4 A. 3 B. 6 C. 12 D. 2 10. f (x)= A. - 2 B. 2 C. 1 D. - 1 C. Solve what is asked in the following problems. Write your solutions and final answers on a separate sheet. Tangent and normal lines are drawn to the curve y = x' at x = 2. 11. What is the equation of the line tangent to the curve at the given point? A. y = 12x - 16 C. y = x - 12 B.y = x - 16 D. y = 12x 12. What is the equation of the normal line drawn to the curve at the given point? A. y = + C. y = 2+49 B. y = 2+98 12 D. y = x +98 Mr. dela Cruz encourages his students to solve Math problems fast and with accuracy. He observed in his Math class that the time it takes a student to solve x word problems is defined by the function f(x) = 3x - x where f(x) is in minutes. 13. Find the average rate of change in solving time from 1 to 3-word problems. A. 6 minutes/problem C. 11 minutes/problem B. 21 minutes/problem D. 25 minutes/problem 14. Find the average rate of change in solving time from 3 to 5-word problems. A. 5 minutes/problem C. 13 minutes/problem B. 20 minutes/problem D. 23 minutes/problem 15. Solve for the instantaneous rate of change in solving time at 2-word problems. A. 6 minutes/problem C. 11 minutes/problem B. 21 minutes/problem D. 26 minutes/