Year 11 Maths - Methods Applications of differentiation and antidifferentiation of polynomials

Rates Of Change

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Questions

Question 1

29183

Given \(f(x) = {x^2} + 3x\), find the average rate of change for \(x \in [2,2 + h]\)

Answer

\(7+h\)

Worked Solution

\begin{aligned}
\text { Average rate of change } &=\frac{f(2+h)-f(2)}{2+h-2} \\
&=\frac{(2+h)^{2}+3(2+h)-(4+6)}{h} \\
&=\frac{4+4 h+h^{2}+6+3 h-10}{h} \\
&=\frac{7 h+h^{2}}{h} \\
&=7+h
\end{aligned}

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