Calculus For Business Assessment 2

1. Differentiate the following with respect to x a) y5x2 4x-6 b) y2x(1-x) c) y2/x3 -x d) y 3sqrt x - 3x4 e) yxFrind the gradient of the tangent to y3x4 - 4x3 at the point (1, -1) b) yx1/2 -x-1/2 at the point (4,3/2) 3) A manufacturer estimates that the hourly cost of producing x units of a product on an assembly line is C(x) 0.1x3 -6x2 136x 200 dollars. a) Compute C(21) - C(20), the extra cost of raising the production from 20 - 21 units. b) Find the marginal cost when the production level is 20 units, C(20). 4) a) sketch the curve y x2 -4x b) Differeniate y x2 -4x. c) Find the gradient of the curve at the points where it croses the x axis. 5) The Revenue from producing (and selling) x units of a product is given by R(x) 3x - 0.01x2 dollars a) Find the marginal Revenue function. b) Compute the marginal revenue at a production level of 20 units and explain what this represents. c) Find the production level x, when the revenue is 20 1.) a) EMBED Equation.3 b) EMBED Equation.3 c) EMBED Equation.3 d) EMBED Equation.3 e) EMBED Equation.3