When does $3x^4-16x^3+18x^2=k$ have exactly two real roots?
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Ref: R6537

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Question

Find the coordinates of each turning point on the graph of $y=3x^4-16x^3+18x^2$ and determine in each case whether it is a maximum point or a minimum point.

Sketch the graph of $y=3x^4-16x^3+18x^2$, and state the set of values of $k$ for which the equation $3x^4-16x^3+18x^2=k$ has precisely two real roots for $x$.

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Calculus meets Functions

When does $3x^4-16x^3+18x^2=k$ have exactly two real roots? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

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When does $3x^4-16x^3+18x^2=k$ have exactly two real roots?
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