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

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