The relationship between f and g is given. Explain the

Clifton Sanchez 2021-11-20 Answered
The relationship between f and g is given. Explain the relationship between f′ and g′
\(\displaystyle{g{{\left({x}\right)}}}={2}{f{{\left({x}\right)}}}\)

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

Sculd1987
Answered 2021-11-21 Author has 1043 answers
Step 1
Given g(x)=2f(x).........(1)
we have to find the relation between their respective derivatives g'(x) and f'(x)
Step 2
Differentiating (1) with respect to x,
\(\displaystyle{\frac{{{d}{\left\lbrace{g{{\left({x}\right)}}}\right\rbrace}}}{{{\left.{d}{x}\right.}}}}={\frac{{{d}{\left\lbrace{2}{f{{\left({x}\right)}}}\right\rbrace}}}{{{\left.{d}{x}\right.}}}}\)
\(\displaystyle\Rightarrow{g}'{\left({x}\right)}={2}{\frac{{{d}{\left\lbrace{2}{f{{\left({x}\right)}}}\right\rbrace}}}{{{\left.{d}{x}\right.}}}}\)
=2f'(x)
Hence g' is 2 times f'.
Have a similar question?
Ask An Expert
0
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-05-01
g is related to one of the parent functions described in Section 1.6. Describe the sequence of transformations from f to g. g(x) = √3x
asked 2021-06-12
g is related to one of the parent functions described in Section 1.6. Describe the sequence of transformations from f to g. g(x) = 2 ||x + 5||
asked 2021-05-13
g is related to one of the parent functions. Describe the sequence of transformations from f to g. g(x) = -2|x - 1| - 4
asked 2021-09-20
Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval.
\(\displaystyle{g{{\left({x}\right)}}}={2}\sqrt{{{3}}}-{x},{\left(-\infty,{3}\right]}\)
asked 2021-08-08
Graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range.
\(\displaystyle{f{{\left({x}\right)}}}={3}^{{{x}}}\) and \(\displaystyle{g{{\left({x}\right)}}}=-{3}^{{{x}}}\)
asked 2021-08-16
For each of the following functions f (x) and g(x), express g(x) in the form \(\displaystyle{a}:{f{{\left({x}+{b}\right)}}}+{c}\) for some values a,b and c, and hence describe a sequence of horizontal and vertical transformations which map \(\displaystyle{f{{\left({x}\right)}}}\ \to\ {g{{\left({x}\right)}}}.{\left({a}\right)}{\left({i}\right)}\)
\(\displaystyle{f{{\left({x}\right)}}}={x}^{{{2}}},{g{{\left({x}\right)}}}={2}{x}^{{{2}}}+{4}{x}\)
\(\displaystyle{\left({i}{i}\right)}{f{{\left({x}\right)}}}={x}^{{{2}}},{g{{\left({x}\right)}}}={3}{x}^{{{2}}}-{24}{x}+{8}\)
\(\displaystyle{\left({b}\right)}{\left({i}\right)}{f{{\left({x}\right)}}}={x}^{{{2}}}+{3},{g{{\left({x}\right)}}}={x}^{{{2}}}-{6}{x}+{8}\)
\(\displaystyle{\left({i}{i}\right)}{f{{\left({x}\right)}}}={x}^{{{2}}}-{2},{g{{\left({x}\right)}}}={2}+{8}{x}-{4}{x}^{{{2}}}\)
asked 2021-09-30
Given that f(x) = 3x - 7 and that (f + g)(x) = 7x + 3, find g(x).
...