Apps. and Interpretation for IBDP Maths Ebook 1 | Page 209

(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 ( � 1) .
[3]
[2]
(ii) Find the value of f �( � 1) .
(iii)
Hence, write down the gradient of the line perpendicular to the tangent at
x �� 1.
15
(iv) Find the equation of normal at x �� 1, giving the answer in slopeintercept
form.
(v)
Find the x -intercept of the normal.
[8]
32
3. Let f ( x) �125x
� , where x � 0 .
2
x
(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 interval of x when f( x ) is decreasing.
(e) (i) Write down the value of f (1) .
[1]
[2]
[3]
[2]
(ii) Find the value of f � (1) .
(iii) Hence, find the equation of tangent at x � 1, giving the answer in general
form.
[5]
(f) The equation f ( x)
� k has only one solution. Write down the range of values of
k .
[2]
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