Calculus Question

1.

Use logafithmic differentiation to find the derivative of the following function 3 85x 3231' +23: y _ 111(4x3 + 2x2)\\ix3 + 2x E\" E" For the functiony = 6x5 + 103i:3 + 1 Use derivative tests and/or sign diagrams to determine the following {2 marks} Where the graph is increasing and decreasing {2 marks} The coordinate of turning points, indicates if it is a maximum or a minimum {2 marks} Where the graph is concave up and concave down {2 marks} The coordinates of point of inflections 2 fV4x+5dx 0 a) (2 marks) Use trapezoidal rule with n = 4 to approximate the integration b) (4 marks) Estimate the error associated with the approximation in part a. c) (2 marks) Determine the number of subinterval (n) needed to achieve error less than 10'5