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Calculus of Powers

Review question

If we increase $x$ by a small amount, what happens to $y$?
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Ref: R9942

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Question

Given that \(y = 4x^3 - 7x^2\), find the value of \(dy/dx\) at the point \((2,4)\).

Hence find the approximate increase in \(x\) which will cause \(y\) to increase from \(4\) to \(4.05\).