The graph shows $y=x^3$. Near the origin the curve flattens, and its tangent there is horizontal.

Question

The graph shows $y=x^3$. Near the origin the curve flattens, and its tangent there is horizontal. State the gradient of the tangent at the origin.[1] Mina says, “A tangent never crosses its curve.” Explain how this graph contradicts her claim.[2]

Accepted Answer

(a) 0. (b) The curve changes sides of its horizontal tangent at the origin.

A tangent that crosses its curve

A tangent that crosses its curve

Solution:

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