Calculate the derivatives of the functions. Then find the values of the derivatives as specified. f(x)=4-x^{2}; f'(-3),f'(0),f'(1)

York 2021-02-14 Answered
Calculate the derivatives of the functions. Then find the values of the derivatives as specified.
\(\displaystyle{f{{\left({x}\right)}}}={4}-{x}^{{{2}}};{f}'{\left(-{3}\right)},{f}'{\left({0}\right)},{f}'{\left({1}\right)}\)

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Expert Answer

Nathanael Webber
Answered 2021-02-16 Author has 21884 answers
Step 1
Given function
\(\displaystyle{f{{\left({x}\right)}}}={4}-{x}^{{{2}}}\)
To find the derivative , the derivative given below is used
\(\displaystyle{f}'{\left({x}^{{{n}}}\right)}={n}{x}^{{{n}-{1}}}\)
So the derivative of given function is
\(\displaystyle{f}'{\left({x}\right)}=-{2}{x}\)
Step 2
The values of specified derivatives are
\(\displaystyle{f}'{\left({x}\right)}=-{2}{x}\)
\(\displaystyle{f}'{\left(-{3}\right)}=-{2}\times-{3}\)
=6
\(\displaystyle{f}'{\left({0}\right)}=-{2}\times{0}\)
=0
\(\displaystyle{f}'{\left({1}\right)}=-{2}\times{1}\)
=-2
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