Differentiation and applications ( * )

Please answer the questions on the attachment below. ( ON PAPER/WRITTEN ) ( Please keep solving and explanation seperate)

Differentiation 1 If A = (3, 7) and B = (9, 4), find: a the gradient of AB b the equation of AB. 2 Evaluate the following. a lim(5x+2) x2 -4 b lim X-+2 x-2 3 Differentiate the following with respect to x. a y= 3x by= 8x + 10 C y=x(x+4) d y= - 2x5 +x4 x2 4 If y = 3x - 4x + 8, find - atx =1. dx 5 If f(x) = 4x -x2, find: a f(x) b f(3) c x such that f'(x) = 0. 6 Consider y=x2 + 2x +4. Find the coordinates of the point where the gradient of the tangent to the curve is 6. 7 Consider the graph of the function y =x2. State the values of x for which the function has: a a positive slope b a negative slope c a zero slope. 8 The points A and B lie on the curve of y = 3x - x2. If the x-values of the coordinates of A and B are 1 and (1 + h) respectively, find the gradient of the chord AB. 9 Consider the function y= 1-x, x