Question

A local maximum of the function f(x) occurs for which x-value?

A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 16, negative 2, 0, 6, 0, negative 2.

Answer 1

There is a local maximum at the point (-1,6), therefore, for x = -1

What is a Function ?

A function is a mathematical statement that builds relation between a dependent and an independent variable.

The value of x and y is

x         y

-4        16

-3          -2

-2          0

-1           6

0           0

1           -2

Near a maxima on either side , the value is smaller than the maxima

The function has smaller values than 6 to the left of x = -1, and to the right of it:

Value of function to the left of the maxima

(-3, -2), (-2, 0)

Value of function to the right of the maxima

(0, 0), and (1, -2)

therefore,  (-1, 6) is a maximum,  for x = -1.

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