The function, f, is given by the formula f (x) = x² + kx, where k is a positive constant. The tangent to the line y = f (x), at the point with abscissa x = k, intersects the axis Ox at point A and the axis Oy at point B.The surface of triangle AOB is 36 square units.Find the value of the constant k.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The function, f, is given by the formula f (x) = x² + kx, where k is a positive constant. The tangent to the line y = f (x), at the point with abscissa x = k, intersects the axis Ox at point A and the axis Oy at point B.The surface of triangle AOB is 36 square units.Find the value of the constant k.
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