Question

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

Modeling data distributions
ANSWERED
asked 2021-02-12
Solve and give the correct answer with using second derivative of the function as follows \(\displaystyle f{{\left({x}\right)}}={\left({x}+{9}\right)}^{2}\)

Answers (1)

2021-02-13
The given function is \(\displaystyle f{{\left({x}\right)}}{i}{s}{\left({x}+{9}\right)}^{2}.\)
Obtain the first and second derivative of the function as follows.
\(\displaystyle f{{\left({x}\right)}}={\left({x}+{9}\right)}^{2}\)
\(\displaystyle{f}'{\left({x}\right)}={2}{\left({x}+{9}\right)}\)
\(\displaystyle{f}'{\left({x}\right)}={2}\)
Find the critical points as follows
\(\displaystyle{f}'{\left({x}\right)}={0}\)
\(\displaystyle{2}{\left({x}+{9}\right)}={0}\)
\(\displaystyle\frac{{{2}{\left({x}+{9}\right)}}}{{2}}=\frac{0}{{2}}\)
\(\displaystyle{x}=-{9}\)
Thus, the function has critical point at \(\displaystyle{x}=-{9}\)
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 \(\displaystyle{\left(–{9},{0}\right)}.\)
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