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Question 1 A car moved distance S meters in a time t seconds, according to the formula S = 313+4t278i+4. Determine: 1.1 velocity at (i) t = 0, (mt = 2.55. (4) 1.2 Acceleration at (i) 1' = 0, (int = 2.58. (4) Question 2 Let f(x) = 75x2 , 2x + 6 2.1 Find the equation of the tangent at X = 'l . (5) 2.2 Determine the equation of the normal to the tangent line at X = 1 . (3) Question 3 _ 2:72 If f(X) _ m 3.] Determine the equation of the tangent at X = 1 . (6) 3.2 Determine the equation of the normal to the tangent line at X = 1 . (3) Question 4 Determine the derivative of the following functions with respect to the independent variables: 4.1 y = 7x4 sin(x2 , 1). (3) _ 2(is ) 4.2 y _ %. (3) Question 5 Use logarithm differentiation techniques to determine the y\" of the following functions: 5.] y = \"I'lllellmeliSXll' (4) x2 sin(3x1) 5.2 y = gs-2 (4) Question 6 Determine the derivatives of the following inverse trigonometry functions 6.1 f(x) = tan" x + 3x2. (3) 34 MAT150'II'101/0/2022 6.2 h(t) = 73'/7r+4cosz(ir(e2')). (3) Question 7 Use implicit differentiation to determine % in the following equations: 7.] x2)!2 , 3):)! + 4xy3 = 4. (2) 7.2 x2 +y3 = 27xy. (3) [TOTAL: 50]