ossidianaZ

2021-02-12

Solve and give the correct answer with using second derivative of the function as follows $f\left(x\right)={\left(x+9\right)}^{2}$

Clara Reese

The given function is $f\left(x\right)is{\left(x+9\right)}^{2}.$
Obtain the first and second derivative of the function as follows.
$f\left(x\right)={\left(x+9\right)}^{2}$
${f}^{\prime }\left(x\right)=2\left(x+9\right)$
${f}^{\prime }\left(x\right)=2$
Find the critical points as follows
${f}^{\prime }\left(x\right)=0$
$2\left(x+9\right)=0$
$\frac{2\left(x+9\right)}{2}=\frac{0}{2}$
$x=-9$
Thus, the function has critical point at $x=-9$
Since the second derivative is a constant function and is greater than zero for all values of x, the function has only local minima.
Thus, the function has local minima or minimum at $\left(–9,0\right).$

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