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## Homework Statement

The diagram shows the graph of the curve C whose equation is [tex] y = x(x-1)(x-2) [/tex]

a) find the equation of the tangent at the pont P whose x coordinate is [tex] \frac{1}{2} [/tex]

b) show that the point Q(2,0) lies on the tnagent and on C.

c) Find the shaded area.

the equation of the tangent line is [tex] y = -\frac{1}{4}x +\frac{1}{2} [/tex]

But I am not sure how to work out the shaded area?

Is it the line minus the x-axis?

[tex] \int_\frac{1}{2}^2 -\frac{1}{4}x + \frac{1}{2} -( \frac{3}{2}) [/tex] [tex] dx [/tex]

?

https://www.physicsforums.com/attachment.php?attachmentid=18690&d=1241015314

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