Apps. and Interpretation for IBDP Maths Ebook 1 | Page 202

Your Practice Set – Applications and Interpretation for IBDP Mathematics
(c) Find the value of x such that the gradients of f( x ) and gx ( ) are the same.
(d) Write down the value of g� ( x)
when the gradients of f( x ) and gx ( ) are the
same.
[2]
[1]
2. Consider the function
3 2
f ( x) � x � x � 10 and g( x) �5� x .
(a) Find the expression of f� ( x)
.
(b) Write down the expression of g� ( x)
.
(c) Find the values of x such that the gradients of f( x ) and gx ( ) are the same.
(d)
[3]
Write down the x -coordinate of the mid-point of AB , where A and B are the
points on f( x ) such that the gradients of f( x ) and gx ( ) are the same.
[2]
[1]
[1]
3. Consider the function
f ( x) 24x x
3
� � and
g( x)
3
� .
x
(a) Find the expression of f� ( x)
.
(b) Write down the expression of g� ( x)
.
(c) Find the values of x such that the gradients of f( x ) and gx ( ) are the same.
[3]
(d) A and B are the points on gx ( ) such that the gradients of f( x ) and gx ( ) are
the same. Find the gradient of AB .
[2]
[1]
[2]
4. Consider the function
f ( x) 5
g x
2
� � ax and ( ) 4
�� x , where a � 0 .
(a) (i) Write down the expression of f� ( x)
in terms of a .
(ii) Write down the expression of g� ( x)
.
(b) The gradients of f( x ) and gx ( ) are the same at x � 2 . Find the value of a .
(c) Write down the value of f (2) .
(d) Find the x -intercept of the tangent to f( x ) at x � 2 .
[2]
[2]
[1]
[2]
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