p.lease answer the following questions in math, answers are given however i need to show my work. Plea,se make sure the handwriting is readable. Thank you so so much and God bless!

Q.7 In each case, find the derivative - from first principles. a y = 6 - 7x by = x + 1 - 1 cy = 3x2 Answers: - 7 a -7 2 b. c. 6r (x - 1)2 .8.) Determine the slope of the tangents to y = 2r2 - 4x when x = 0, x = 1, and x = 2. Solution Slope whenx = 0 slope when x = 1 / slope when=2 Fund Slope of Tangent f ( x ) = A r- 8.) (0) = -4:5(1) = 0;f'(2) = 4 Q9.) Calculate the slopes of the tangents to f(x) = x' at points with x-coordinates -2, - 1, 0. 1, 2. Solution shape Slope stape slope 4= 213 when 1=-2 when HE - 1 when H= O Whenk = 1 Find the slope of Tangent ( Derivative ) f ( ) = scape when ) = 2 f'(-2) = 12:f(-1) = 3; Am. 9) "(o) = 0;/'(1) = 3:1"(2) = 12 10, An object moves in a straight line with its position at time f seconds given by s(1) = -1- + 81, where s is measured in metres. Find the velocity when 1 = 0, 1 = 4, and t = 6. Solution AS distance Velocity V(t ) - 5 ( 4) / Velocity Vit)= S(4)/ Velocity V(t)= s'(t) Note: velocity - t Time when t= 0 When t= 4 whent= 6 :. Slope of( s-t ) graph gives Average Velocity Fund the Slope of Tangent at a Point (Derivative) V ( + ) = 5 (+ ) = Aws: 10) s'(0) = 8 m/s; s'(4) = 0m/s; S'(6) = -4 m/sC 4.) Apply the differentiation rules you learned in this section to find the derivatives of the following functions: a y = 3x b) y = 4x - 9 c.) y = + - 3 d.) y = 9x-2 + 3V/x e) v = Vx+ 6VP + V2 Answers . - d. -18x3+ 2x-1 4. a. 5x b. -2r 1+ 61-2 e. ( x ) + 91 1 C. -18 5. Let s represent the position of a moving object at time /. Find the velocity. v = ds at time f. a s = -212 + 71 b.) s = 18 + 51 c) s = (1 - 3) 2 Aws. 5. a. -4r+7 b. 5- c. 21 - 66.) Determine f'(a) for the given function f(x) at the given value of a. a.) f(.x ) = x - Vx,a = 4 "b) f(x) = 7 - 6Vx + 5x, a = 64 AM 6. a. 47.75 b. 24 Q 7) Determine the slope of the tangent to each of the curves at the given point. a) y = 3x4. (1, 3) by = -5 (-1. -1) c) y = =(-2. -1) d) y = V16x . (4, 32) Aww 7. a. 12 c. b. 5 d. 12 Q 8. Determine the slope of the tangent to the graph of each function at the point with the given x-coordinate. a y = 2r' + 3x, x = 1 b ) y' = 2 V x +5, x = 4 Q V = 16 2:*=-2 dy = x (x + 1 ),x = 1 8. a. 9 Aw C. 4 d. -7Q. 9. Write an equation of the tangent to each curve at the given point. 5( x ) 9 a.) y = 2x - -. P(0.5, -1)/7 (xx, , 4,) $ ( # ) 3 4 Solution: by= 27 -, P( - 1. 7 ) > ( x , , 8 , ) Find Slope m using Derivative s (") solution. 5( xx ) = Find slope on using Derivative f (x) f ( x ) = Find the Equation of Tangent Ford the Equation of Tangent y - 4, = m (x-x, ) y-y = m (x- x) ) Aws: 9. a. br - y - 4 = 0 An: b. 18x - y + 25 = 0 c.) y = V3x3, P(3, 9) (x, , 4, ) Solution : Fund Stape musing Derivative f (20 12 + 1), P(1. 2)/ ( x, , 4.) Solution!- S( x) = Find scope m using Derivative f (x) f ( xx ) = Find the Equation of Tangent Find the Equation of Tangend 4= 4, = m(x-X,) y- 8, =m (x-x,) Aruy c.) 9x - 2y - 9 = 0 Ans: d/ sty - 3=0