kironiawalkerm
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The maximum value of the function: f(x)= -5 x ^2 +30x-200 is?

Sagot :

Nayefx

Answer:

[tex] \displaystyle - 155[/tex]

Step-by-step explanation:

we are given a quadratic function

[tex] \displaystyle f(x) = - 5 {x}^{2} + 30x - 200[/tex]

we want to figure out the minimum value of the function

to do so we need to figure out the minimum value of x in the case we can consider the following formula:

[tex] \displaystyle x _{ \rm min} = \frac{ - b}{2a} [/tex]

the given function is in the standard form i.e

[tex] \displaystyle f(x) = a {x}^{2} + bx + c[/tex]

so we acquire:

  • b=30
  • a=-5

thus substitute:

[tex] \displaystyle x _{ \rm min} = \frac{ - 30}{2. - 5} [/tex]

simplify multiplication:

[tex] \displaystyle x _{ \rm min} = \frac{ - 30}{ - 10} [/tex]

simply division:

[tex] \displaystyle x _{ \rm min} = 3[/tex]

plug in the value of minimum x to the given function:

[tex] \displaystyle f (3)= - 5 {(3)}^{2} + 30.3 - 200[/tex]

simplify square:

[tex] \displaystyle f (3)= - 5 {(9)}^{} + 30.3 - 200[/tex]

simplify multiplication:

[tex] \displaystyle f (3)= - 45 + 90- 200[/tex]

simplify:

[tex] \displaystyle f (3)= - 155[/tex]

hence,

the minimum value of the function is -155

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