Please do all the questions

1. For the given linear function, determine the value of derivative f'(a) for the given value of a. a) f(x) = 3x - 5, a = -4 b) f (x) = -6x + 5, a = -3 c) Do you notice a connection between derivative f'(a) and the equation of linear function f (x)? Why does this happen? 2. For the given function, determine the value of derivative f'(a) for the given value of a. a) f(x) = x2+1, a =2 b) f(x) = 4x3 + x, a =-1 c) f (x) = V3x - 2, a = 1 d) f ( x ) = -, a=0 3. Determine the derivative, f'(x), of the following functions using first principles. a) f(x) = 3 - 5x b) f ( x ) = x+3 x-2 c) f(x) = Vx+10 d) f (x) = x3 - 2x 4. Determine the derivative, -, of the following functions using the definition of the derivative. a) y = -2x +7 b) y = 2x+5 4x-1 c) y = v3x - 5 d) y = 4x2 - 8x + 1 5. Determine the slope of the tangent to the graph of the function at the given point. a)y = -x+4, a =1 b) y = 3x+3 Bx-3: 0 = -1 c) y = v-x+8, a =4 d) y = x - 2x, a =0 6. Use the definition of the derivative to show that the following functions are not differentiable at the given value of a. a) f(x) = x3+1 when x = 0 b) f (x) = (x - 2)3 when x = 2 c) f (x) = x -1,if x 2 : When x = 2 d) f (x) = vx +5 when x = -5 e) f (x) = |x - 31, when x = 37. A football is kicked up into the air. Its height, h, above the ground, in metres, at / seconds can be modelled by h(t) = 18t - 4.9t2 a) Determine h'(t). What does this derivative represent? b) Determine h'(2). 8. Determine where the function f(x) = 4x3 - 9x2 - 12x + 4 has a horizontal tangent. 9. Find the point(s) on the curve y = = such that the tangent lines are parallel to the line x+1 x - 2y = 2. 10. Determine the equation of the tangent(s) to f(x) = x2 + 2x + 1 that passes through the point (-2, -8)