ossidianaZ

2021-02-12

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

Clara Reese

Skilled2021-02-13Added 120 answers

The given function is $f\left(x\right)is{(x+9)}^{2}.$

Obtain the first and second derivative of the function as follows.

$f\left(x\right)={(x+9)}^{2}$

${f}^{\prime}\left(x\right)=2(x+9)$

${f}^{\prime}\left(x\right)=2$

Find the critical points as follows

${f}^{\prime}\left(x\right)=0$

$2(x+9)=0$

$\frac{2(x+9)}{2}=\frac{0}{2}$

$x=-9$

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$(\u20139,0).$

Obtain the first and second derivative of the function as follows.

Find the critical points as follows

Thus, the function has critical point at

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