A curve is y=(x-1)2. A student notes that the average gradient from x=0 to x=2 is zero and concludes

Question

A curve is y=(x-1)2. A student notes that the average gradient from x=0 to x=2 is zero and concludes that the curve has zero gradient everywhere between these inputs. Use the derivative and the endpoint values to assess the claim.

Accepted Answer

The claim is false: the derivative is $2(x-1)$ and is zero only at $x=1$.

A zero average gradient

A zero average gradient

Solution:

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