SOLUTION: Suppose that A, B, C, and D are constants and f is the cubic polynomial f(x)=Ax�+Bx�+Cx+D. Suppose also that the tangent line to y = f(x) at x = 0 is y = x and the tangent line at

Question 350591: Suppose that A, B, C, and D are constants and f is the cubic polynomial f(x)=Ax�+Bx�+Cx+D. Suppose also that the tangent line to y = f(x) at x = 0 is y = x and the tangent line at x = 2 is given by y = 2x � 3. Find the values of A, B, C, and D. Then sketch the graph of y = f(x) and the two tangent lines for -2 ≤ x ≤ 4.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

The slope of the tangent line at a given point is the value of the derivative at that point.
The derivative of the function is,

At x=0, the slope of the tangent line is .

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At x=2, the slope of the tangent line is .

1.
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Using the tangent line at x=0, you also know the intersection point because,

(0,0) is also a point on the cubic.

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Similarly at x=2,

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2.
Subtract eq. 2 from eq. 1,

Then from eq. 2,

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