Find the values of b such that the function has the given maximum or minimum val

Khaleesi Herbert 2021-09-08 Answered
Find the values of b such that the function has the given maximum or minimum value.
\(\displaystyle{f{{\left({x}\right)}}}=-{x}^{{{2}}}+{b}{x}-{75}\); Maximum value: 25

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

Macsen Nixon
Answered 2021-09-09 Author has 14118 answers
The maximum or minimum of a quadratic function \(\displaystyle{y}={a}{x}^{{{2}}}+{b}{x}+{c}\) occurs at the vertex which has an x-coordinate given by:
\(\displaystyle{x}=-{\frac{{{b}}}{{{2}{a}}}}\)
From the given, a=-1 and b=b sp we have:
\(\displaystyle{x}=-{\frac{{{b}}}{{{2}{\left(-{1}\right)}}}}={\frac{{{b}}}{{{2}}}}\)
Since a=-1
\(\displaystyle-{\left({\frac{{{b}}}{{{2}}}}\right)}^{{{2}}}+{b}{\left({\frac{{{b}}}{{{2}}}}\right)}-{75}={25}\)
Solve for b:
\(\displaystyle-{\frac{{{b}^{{{2}}}}}{{{4}}}}+{\frac{{{b}^{{{2}}}}}{{{2}}}}-{75}={25}\)
\(\displaystyle{\frac{{{b}^{{{2}}}}}{{{4}}}}={100}\)
\(\displaystyle{b}^{{{2}}}={400}\)
\(\displaystyle{b}=\pm\sqrt{{{400}}}\)
\(\displaystyle{b}=\pm{20}\)
Result:
\(\displaystyle{b}=\pm{20}\)
Have a similar question?
Ask An Expert
38
 

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 2021-09-15
Find the values of b such that the function has the given maximum or minimum value.
\(\displaystyle{f{{\left({x}\right)}}}=-{x}^{{2}}+{b}{x}-{75}\)
Maximum value: 25
asked 2021-01-13

find the values of b such that the function has the given maximum or minimum value. \(f(x) = -x^2+bx-75\), Maximum value: 25

asked 2021-08-03
For each of the following, find the maximum and minimum values attained by the function f along the path c(t):
(b) \(\displaystyle{f{{\left({x},{y}\right)}}}={x}^{{2}}+{y}^{{2}}.{c}{\left({t}\right)}={\left({\cos{{t}}},{2}{\sin{{t}}}\right)}{.0}\leq{t}\leq{2}\pi\)
asked 2021-07-31
For each of the following, find the maximum and minimum values attained by the function f along the path c(t):
(a) \(\displaystyle{f{{\left({x},{y}\right)}}}={x}{y}.{c}{\left({t}\right)}={\left({\cos{{t}}},{\sin{{t}}}\right)}.{0}\leq{t}\leq{2}\pi\)
asked 2021-06-06
For each of the following, find the maximum and minimum values attained by the function f along the path c(t):
(a) \(f(x,y) = xy. c(t) = (cost,sint). 0 \leq t \leq 2 \pi\)
asked 2021-05-12
Find the absolute maximum and absolute minimum values of f on the given interval and state where those values occur: \(f(x)=x^{3}-3x^{2}-9x+25, [-5,10]\)
asked 2021-05-09
Find the absolute maximum and minimum values of f on the given interval.
\(f(x)=4x^{3}-6x^{2}-24x+9. [-2,3]\)
...