Year 11 Maths - Methods Differentiation and antidifferentiation of polynomials

Instantaneous rate of change

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Questions

Question 1

84383

For \(y=x^3-x\), estimate the instantaneous rate of change of \(y\) with respect to \(x\) when \(x=1\)

Answer

\(\approx 2\)

Worked Solution

\begin{align}
\text{For }x \in [1,1.1]&\\
\text{Average rate of change}&=\frac{(1.1^3-1.1)-(1^3-1)}{1.1-1}\\
&=2.31\\
\therefore\, \text{ Instantaneous rate} &\approx 2
\end{align}

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