Apps. and Interpretation for IBDP Maths Ebook 1 | Page 210

Your Practice Set – Applications and Interpretation for IBDP Mathematics
4. Let
f ( x)
1 8
2 x
2
� x � , where 0
2
x � and x �� 1.
(a) Write down the equation of the vertical asymptote of the graph of f .
(b) Find f� ( x)
.
(c) Find the coordinates of the local minimum point of the graph of f .
(d) Write down the intervals of x when f( x ) is increasing.
(e) (i) Write down the value of f (4) .
[1]
[2]
[3]
[2]
(ii) Find the value of f � (4) .
(iii)
Hence, write down the gradient of the line perpendicular to the tangent at
x � 4 .
(iv) Find the equation of normal at x � 4 , giving the answer in slope-intercept
form.
[6]
(f) The equation f ( x)
� k has no solution. Write down the range of values of k .
[2]
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