Question
Determine whether the function $\mathrm{y}=3+2 \mathrm{x}-7 \mathrm{x}^2$ is increasing or decreasing at $\mathrm{x}=-4$ and $\mathrm{x}=4$.
✓
Answer
$y=3+2 x-7 x^2$
$\therefore \frac{d y}{d x}=0+2(1)-7(2 x)$
$=2-14 x$
$\text { At } x=-4, \frac{d y}{d x}=2-(14)(-4)$
$=2+56=58>0$
So, at $x=-4$ function is increasing.
At $x=4, \frac{d y}{d x}=2-(14)(4)=2-56=-54<0$
So, at $x=4$ function is decreasing.
$\therefore \frac{d y}{d x}=0+2(1)-7(2 x)$
$=2-14 x$
$\text { At } x=-4, \frac{d y}{d x}=2-(14)(-4)$
$=2+56=58>0$
So, at $x=-4$ function is increasing.
At $x=4, \frac{d y}{d x}=2-(14)(4)=2-56=-54<0$
So, at $x=4$ function is decreasing.
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