Homework 2.1-2.4 Due Thurs. 9/15 beginning of class Compute the derivative function, f'(x), using the definition of derivative for each of the following. Use proper notation. f'(x) = lim /(*th)-f(x) h=0 h 1. f(x) = 3x2 +1 2. f (x ) = 2 Compute f'(c) for each of the following using the alternate form of the definition of the derivative. f' (c) = lim f (c + h) - f (c ) h - h 5. f(x) =3x+1, c=1For Problem 7 & 8, the given limits represent an f'(c) for a function f(x) and a number c. Find fand c. 5-3(1 + Ax) |- 2 7. lim Ax 8. lim (-2 + Ax) +8 Ax For Problems 9 and 10, consider the sketch of the function, f (x), to the right. (4, 5) 9. a.) Find f (1) and f (4). b.) Calculate f (4) -f (1). (1, 2) c.) What does the equation y = f (4) -J() (x- 1) + f(1) represent? 4-1 10. Insert the proper inequality symbol () between the given quantities. If you need help, draw the represented line in the picture above a. ) f ( 4) - f(1) f (4) - f(3) b.) f ( 4) - f(1) f' ( 1) 4-1 4-3 4-11. 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. Label correctly. b.) Estimate the derivative of fat x = 40rps. Label correctly. 1.) For the following, state whether the function is continuous, differentiable, both or neither at x = c. b) c) d) C e) g) h) C C2.) Sketch a function having the following attributes, if possible. a.) differentiable and b.) continuous, but not continuous at the point c.) cusp at (-1, 3) d.) differentiable, but not (2,4) differentiable at (-3, 1) continuous at (2,-4) MCQ Practice 3.) Let the function f be continuous on a S x 3 b but not differentiable for some c such that a c * -> c X - C (A) I only (B) II only (C) III only (D) I and III only (E) II and III only 5.) If f is a differentiable function such that f (2) = 5 and f'(2) = 7, which of the following statements could be false? (A) lim f (x) = 5 * - 2 (B) lim f(x) = lim f (x) x - 2 - (C) lim f (x) - 5_ x - 2 x - 2 (D) lim f (2+ h) - 5_ 7 h - h (E) lim f'(x) = 7 h -o "