Question

For the curve y = (2x + 1)^3 find the rate of change of slope at x = 1

Answer 1

$$\begin{gathered} \mathrm{y}={\left(2\mathrm{x}+1\right)}^3 \\ \mathrm{On}\mathrm{differentiating}\mathrm{wrt}\mathrm{x},\mathrm{we}\mathrm{get} \\ \mathrm{y}\text{'}=3{\left(2\mathrm{x}+1\right)}^2.2 \\ \mathrm{y}\text{'}=6{\left(2\mathrm{x}+1\right)}^2 \\ \mathrm{Rate}\mathrm{of}\mathrm{change}\mathrm{of}\mathrm{slope}\mathrm{at}\mathrm{x}=1 \\ \mathrm{y}\text{'}=6{\left(2\left(1\right)+1\right)}^2=6{\left(2+1\right)}^2 \\ =6\left(9\right)=54\mathrm{ANS}... \end{gathered}$$