y
5
y = \frac{1}{2}x^2 + x + \frac{5}{2}
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Figure 2
P(1,4)
?x
5
Figure 2 shows the graph \(y = \frac{1}{2}x^2 + x + \frac{5}{2}\) and line \(l\) which is a normal to
the curve at point P(1, 4).
[4]
(a) Find the equation of line \(l\). Give your answer in the form \(y = mx + c\).
(b) Find the area, which is shaded on the diagram, that is bounded by the curve
\(y = \frac{1}{2}x^2 + x + \frac{5}{2}\), line \(l\) and the y – axis.
Give your answer in the form \(\frac{a}{b}\) where a and b are integers.
All working must be shown. Just giving the answer, even the correct one,
will score no marks if this working is not seen.
[4]
(c) Point Q\((\frac{3}{2}, \frac{17}{8})\) lies on the curve \(y = \frac{1}{2}x^2 + x + \frac{5}{2}\).
Explain why the tangent to the curve at point Q cannot intersect with line \(l\).
[4]
