Question

Can Anyone help me this is my last question for webwork?

Answer 1

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Answer:

• maximum: 12
• at x = 0

Explanation:

The x-term has even degree so is never negative. The x-term is subtracted from 12, so the maximum value of the function will be found where x=0. That value is 12 -0 = 12.

f(0) = 12 . . . . absolute maximum

Answer 2

The function
`f(x)=12-6x^4` has an absolute maximum value of
`12` and this occurs at
`x $\ equals 0.`

Explanation:

The maximum value of this function is at 12, because if you rewrite this function:

• 
  `f(x)=-6x^4+12`

The +12 is the k-value (the graph of this function is a parabola) of the vertex form of a quadratic. Just a reminder:

Vertex form of a parabola:

• 
  `a(x-h)^2+k`

You can see the 12 is the k-value. The k-value of the vertex form is the vertical shift of the parabola, meaning that this parabola is shifted 12 units upwards.

Since the parabola opens down (you can tell by the negative a-value
`-6`), there is a maximum value at the k-value, i.e. the vertical shift.

`f(x)=-6x^4+12` has an absolute maximum value of
`12`.

To find where the maximum value occurs at, the formula:

• 
  `-(b)/(2a)`

Tells us the x-value of the vertex of the parabola, whose y-value is the maximum value.

Using our rearranged equation, the a, b, and c-values are:

• 
  `a=-6`
• 
  `b=0`
• 
  `c=12`

Plug in the a and c values into the formula to find the x-value of the maximum point:

• 
  `-(b)/(2a)`
• 
  `-((0))/(2(-6))=0`

Therefore, the absolute maximum value of 12 occurs at x = 0.