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| Math Central | Quandaries & Queries |
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Question from Jay, a student: For what values of a and b will the parabola y = x^2 + ax + b be tangent to the curve y = x^3 at (1,1)? |
Hi Jay,
If each of the curves has a tangent at (1,1) then each curve must pass through (1,1). Substitute x = 1, y = 1 into the first equation. This gives you an equation in the variables a and b. If the two curves share a common tangent at this point then dy/dx at x = 1 has the same value for y = x2 + ax + b and y = x3. Find dy/dx for both functions and substitute x = 1. Set the two derivatives equal. Solve for a.
Penny
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