Review Topic 13: Differentiation and applications — Short answer Evaluate the following where possible. where Calculate the following. if if where Identify the subset of the domain of the function where it is: decreasing stationary increasing. Find the equation of the tangent drawn to the graph of at the point where the tangent: a i is parallel to the line ii is parallel to the x-axis. b Obtain the equation of the tangent to the curve at the point where the curve cuts the a Show that the curve has a stationary point at and determine its nature using the slope of the tangent. b Consider the curve . Write down the cubic equation from which the stationary points of are i obtained. ii Given there is a stationary point near , use the Newton–Raphson method to obtain the of this stationary point correct to 4 decimal places. x-coordinate iii Determine the nature of this stationary point. 6 At what rate, with respect to its radius, is the volume of a sphere changing when: the radius is cm the volume is cm3? (The formula for the volume of a sphere is .) Multiple choice
Review — Topic 13: Differentiation and applications Short answer Evaluate the following where possible. where Calculate the following. if if where Identify the subset of the domain of the function where it is: decreasing stationary increasing. a Find the equation of the tangent drawn to the graph of at the point where the tangent: i is parallel to the line ii is parallel to the x-axis. b Obtain the equation of the tangent to the curve at the point where the curve cuts the a Show that the curve has a stationary point at and determine its nature using the slope of the tangent. b Consider the curve . i Write down the cubic equation from which the stationary points of are obtained. ii Given there is a stationary point near , use the Newton–Raphson method to obtain the x-coordinate of this stationary point correct to 4 decimal places. iii Determine the nature of this stationary point. 6 At what rate, with respect to its radius, is the volume of a sphere changing when: the radius is cm the volume is cm3? (The formula for the volume of a sphere is .) Multiple choice
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