IB Mathematics: Analysis & Approaches AA_HL_5.
4(14)_diff_calc6_v1
Calculus 6 (exercise set)
syllabus content: chain rule; product rule; quotient rule; tangent lines; implicit differentiation; points of
inflexion; related rates; optimization
total marks: 94
Part I – No GDC – Questions 1-6
1+ x
3. Consider the function f ( x ) = ln .
1− x
(a) State the domain of the function f. [2 marks]
(b) Find the derivative of f, f ( x ) , and express it in simplified form. [4 marks]
x2 − 3
4. Consider the function g ( x ) = .
2− x
(a) Find g ( x ) . [3 marks]
(b) There are two points, P and Q, on the graph of g where there are horizontal
tangents. Find the equation of the line that passes through P and Q. [7 marks]
5. Consider the function defined by f ( x ) = e x sin x, 0 x π . Determine, with justification, the
coordinates of the point of inflexion of f. [7 marks]
6. A curve has equation 3x − 2 y 2e x −1 = 2
dy
(a) Find an expression for in terms of x and y. [5 marks]
dx
(b) Find the equations of the tangents to this curve at the points where the curve intersects the
line x = 1 . [4 marks]
Part II (Qs 7-11) – calculator allowed
7. The tangent to the graph of the curve y = ax + ln ( 5 − x 2 ) at the point where x = 2 is parallel to the
line x + y + 4 = 0 . Find the value of a. [6 marks]
© InThinking – IB Maths: Analysis 1
IB Mathematics: Analysis & Approaches AA_HL_5.4(14)_diff_calc6_v1
Calculus 6 (exercise set)
11.
© InThinking – IB Maths: Analysis 2
