Name Day 9 Homework- The Definition of the Derivative Compute the derivative function, f'(x), using the definition of derivative for each of the following. Use proper notation. 1. f(x) = 3x +1 2. f (x) = 2 3. f ( x ) = x+1 4. f(x) = V3x+1 Compute f'(c) for each of the following using the alternate form of the definition of the derivative. 5. f(x) =3x+1, c=1 6. f(x) = x+-, c=4For Problem 7 & 8, the given limits represent an f'(c) for a function f(x) and a number c. Find f and c. 7. lim [5-3(1+ 4x)]-2 (-2+Ax) +8 Ar-20 8. lim Ar Ax For Problems 9, consider the sketch of the function, f (x), to the right. 9. a.) Find f(1) and f (4). b.) Calculate f (4)-f (1). ( 4, 5) (1, 2) c.) What does the equation y = 4 - 1 f ( 4 ) - f0 ( x -1) + f (1) represent? 10. The table shows the margin of error in degrees for tennis serves hit at 100 mph with various amounts of topspin (in units of revolutions per second). Topspin (rps) (x) 20 40 60 80 100 Margin of error f(x) 1.8 2.4 3.1 3.9 4.6 a.) Estimate the derivative of fat x = 70 rps. b.) Estimate the derivative of fat x = 40rps. Label Label correctly. correctly. Answers: 1) 6x 2) 0 - 3 3 ) ( x + 1 ) 2 3 2V3x+1 5) 3 6) 3/4 7) f(x) = 5- 3x, C=1 8 ) f ( x ) = x2, C = - 2 9a) f(1) = 2, f (4) = 5 9b ) 3 9c) secant line between (1, 2) and (4, 5) 10a) 0.04 10b) 0.0325