Step 1

From the given data:

Step 2

\(\displaystyle{f{{\left({x}\right)}}}={6}{x}^{{{4}}}−{6}{x}^{{{3}}}\)

Now, differentiating the above equation with respect to x

\(\displaystyle{f}'{\left({x}\right)}={24}{x}^{{{3}}}-{18}{x}^{{{2}}}\)

Now, differentiating the above equation with respect to x

\(\displaystyle{f}{''}{\left({x}\right)}={72}{x}^{{{2}}}-{36}{x}\)

Now, differentiating the above equation with respect to x

f'''(x)=144x-36

From the given data:

Step 2

\(\displaystyle{f{{\left({x}\right)}}}={6}{x}^{{{4}}}−{6}{x}^{{{3}}}\)

Now, differentiating the above equation with respect to x

\(\displaystyle{f}'{\left({x}\right)}={24}{x}^{{{3}}}-{18}{x}^{{{2}}}\)

Now, differentiating the above equation with respect to x

\(\displaystyle{f}{''}{\left({x}\right)}={72}{x}^{{{2}}}-{36}{x}\)

Now, differentiating the above equation with respect to x

f'''(x)=144x-36