Point C is the intersection between the tangent of the curve at A and the tangent of the curve at B:
The diagrams shows the curve , which crosses the at the points , and .
(i) The tangents to the curve at the points A and B meet at the point C. Find the coordinates of C.
(ii) Show by integration that the area of the shaded region is the same as the area of the shaded region .
I can't see the point on the graph!
well first you need to find the gradient of the lines AC and BC, remember that differentiating the equation of the curve will give you the gradient at a particular point:
substituting the coordinates of x given in A(1,0) and B(2,0) you can get the gradient at A and B respectively.
then using the general line equation:
obtain the line equation for AC and BC
then solving the simultaneous equation(equation of line AC and BC) you can get the coordinates of C