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Application [29 Marks] 23. Using first principles, determine the derivative of f (x) = - V4X+7 [5 Marks] 13. Find the torque produced by a cyclist exerting a force of F = [45, 90, 130]N on the shaft- pedal d = [12, 17, 14]cm long. a) (-950, 930, -315) b) 3890 c) 19874 d) 1866625 14. Given a = [3, -1, 4]& c = [-2, 6, t], find t so that a and c are perpendicular. 2) 4 b ) - 3 C) - 4 d) 3 15. Given u = [-12, 6, k]& v = [4, -2, 4], find k so that u and v are parallel. a ) 4 b ) - 3 c) 6 d) -12 16. An object moves along a straight line in such a way that its position is s(t) = -5t3 + 17t2, in which t represents the time in seconds. What is the object's acceleration at 2.7 seconds? a) -47 b) -17.55 c) 17 d) -81 17. Find the unit vector of a = [-3, -7, 4]. a) 74 [-3,-7,4] b) Jig [ - 3, - 7, 4 ] C) [ VIA' VIA' VIA d) VTA' VTA' VTAl 18. Derive y = -2(3-7x) a) -2in3(3-7x) b) -14ln7(3-7x) c) 7in2(3-7x) d) 143(3-7x)