Question

Consider the function f(x) = 2 - 7x ^ 2, - 4 <= x <= 1 The absolute maximum value is and this occurs at x =

Answer 1

Given that

The function is

`f(x)=2-7x^2,\text{ -4}\leq x\leq1`

Explanation -

We have to find the maximum and minimum values of the function at the corresponding value of x.

Then,

`\begin{gathered} Values\text{ of x are -4, -3, -2, -1, 0, and 1} \\ f(1)=2-7*1^2=2-7=-5 \\ f(0)=2-0=2 \\ f(-1)=2-7*(-1)^2=2-7=-5 \\ f(-2)=2-7*(-2)^2=2-7*4=2-28=-26 \\ f(-3)=2-7*(-3)^2=2-7*9=2-63=-61 \\ f(-4)=2-7*(-4)^2=2-7*16=2-112=-110 \end{gathered}`

Hence, the maximum value of f(x) is 2 at x = 0

and minimum value of f(x) is -110 at x = -4

Final answer -

The final answer is the maximum value of f(x) is 2 at x = 0and minimum value of f(x) is -110 at x = -4