MORE POWER LAW PRACTICE 1. Which of the following functions have a 5. A skydiver jumps out of a plane that is flying derivative of zero? 2500 m above the ground. The skydiver's a) y = 9.8 b) y = 11 height above the ground, in metres, after * seconds is b(t) = 2500 -4.9t. d y=-4+x d) y=: a) Determine the rate of change of the height of the skydiver after 5 s. e) y = v7 f) y= x b) The skydiver's parachute opens at 1000 m g) h) y= -2.8x above the ground. After how many seconds does this happen? () What is the rate of change of the height of the skydiver at the time found in part b)? 2. Determine the slope of the tangent to the graph of each function at the indicated value. a) y=6, x = 12 b) /(x) = 2x', x = v3 Answer Key: d g(x) = - 3 VX 1. A, B, E, G, and H all have a derivative of zero since they are all constants. d) b(r) = -4.9t, t= 3.5 e) A(r) = mr, = 3 2. (a) 0 (b) 90 (c) 3/16 (d) -34.3 (e) 3pi/2 (f) -1/12 () y = 1 3.x 3. (1) (0.25, 3.625) ii) (2.5, 5.25) (iii) (-4/3, 5/3) which equals approximately (1.3, 1.6) 3. Determine the point at which the slope of 4. the tangent to each parabola is zero. al f(x) = 5x2 - 3x; ('(x) = 10x - 3 i) y= 6x2 - 3x + 4 b) g(x) = 6x2 + 5x - 4; g'(x) =12x +5 in y= -x2 +5x - 1 i) y = =x2+ 2x + 3x2+2x+3 () p(x) =-x5-x3+1. 7; P'(x) = 2x4 - 3x2 d) f (xx) = 25x2+ 20x+4; f'(x) =50x+20 4. Simplify, and then differentiate. 5 a) f(x) = 10x4- 6x3 -49 m/s b) 17.5 s () 171.5 m/s 2x2 b) g(x) = (3x + 4)(2x - 1) () p(x) = x- 4x6+ 2x3 4x3 d) f (x) =(5x+2)2