2008 (2nd)Course2-4.1
We are to find a function f(x) such that its derivative is x^2+x-1 and the graph of y=f(x) is tangent to the straight line y=x+1.
First we find the coordinates of the point at which y=f(x) and y=x+1 are tangent.Since the slope of the tangent line is A,the x-coordinate of this point satisfies
x^2+x-B=0.
Therefore,the x-coordinate of this point is either CD or E,and hence the required point is either
(CD,FG) or (E,H).
Hence the required function f(x) is either
y=f(x)=1/Ix^3+1/Jx^2-x-K/L .......#1
or
y=f(x)=1/Ix^3+1/Jx^2-x+MN/O .......#2
Furthermore,since the graph of #1 can be obtained by translating the graph of #2 in the direction of the y-axis,the area of the region bounded by the graphs of #1 and #2 and the two straight lines x=CD and x=E is PQ/2.
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