Derivatives

What this lesson shows

y = x². How steep is it… exactly at x = 1? Not on average — at that one single point.

Try it yourself

Real questions from this lesson's worksheets — answers below each one.

1. Slope of y = x² at x = 1
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   2
2. f(x) = x² + 8x + 4. Find f'(1)
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   10
3. Slope of y = x² at x = 2
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   4
4. A car's position after t seconds is s(t) = t² metres. Its velocity is s′(t) = 2t. Find the velocity at t = 3
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   6