Question

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

Answer 1

`\displaystyle - 155`

Explanation:

we are given a quadratic function

`\displaystyle f(x) = - 5 {x}^(2) + 30x - 200`

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:

`\displaystyle x _( \rm min) = ( - b)/(2a)`

the given function is in the standard form i.e

`\displaystyle f(x) = a {x}^(2) + bx + c`

so we acquire:

• b=30
• a=-5

thus substitute:

`\displaystyle x _( \rm min) = ( - 30)/(2. - 5)`

simplify multiplication:

`\displaystyle x _( \rm min) = ( - 30)/( - 10)`

simply division:

`\displaystyle x _( \rm min) = 3`

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

`\displaystyle f (3)= - 5 {(3)}^(2) + 30.3 - 200`

simplify square:

`\displaystyle f (3)= - 5 {(9)}^{} + 30.3 - 200`

simplify multiplication:

`\displaystyle f (3)= - 45 + 90- 200`

simplify:

`\displaystyle f (3)= - 155`

hence,

the minimum value of the function is -155