Year 11 Maths - Methods
Differentiation and antidifferentiation of polynomials
Graphs Of The Derivative Function
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Questions
Question 1
28108
Over what domain interval is the function \(y = \dfrac{1}{3}{x^3} + \dfrac{5}{2}{x^2} + 6x - 2\) decreasing ?
| \begin{align} &\begin{aligned} y &=\frac{1}{3} x^{3}+\frac{5}{2} x^{2}+6 x-2 \\ y^{\prime} &=\frac{1}{3} \times 3 x^{2}+\frac{5}{2} \times 2 x+6 \\ &=x^{2}+5x+6\\ &=(x+3)(x+2) \end{aligned}\\ &\text{Decreasing when }y^{\prime}<0\\ &\therefore(x+3)(x+2)<0\\ &\text{From the graph}\\ &\therefore-3<x<-2 \end{align} |
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