Year 11 Maths - Methods Differentiation and antidifferentiation of polynomials

Instantaneous rate of change

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Questions

Question 1

84380

For \(f(x)=2^x\), estimate the instantaneous rate of change of the function with respect to \(x\) when \(x=1\)

Answer

\(\approx 1.4\)

Worked Solution

\begin{align}
\text{For }x \in [1,1.1]&\\
\text{Average rate of change}&=\frac{f(2^{1.1})-f(2^1)}{1.1-1}\\
&=\frac{2.1435-2}{0.1}\\
&=1.435\\
\therefore\, \text{ Instantaneous rate} &\approx 1.4
\end{align}

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