Question

What is the maximum number of possible extreme values for the function,
f(x) = х2 -7x – 6?

Answer 1

Only one extreme value of f(x) is possible.

Explanation:

We are given the quadratic function of independent variable x which is f(x) = x² - 7x - 6 ......(1)

Now. the condition for extreme values of f(x) is
`(df(x))/(dx) =0`

Hence, differentiating both sides of equation (1) with respect to x, we get

`(df(x))/(dx) = 2x -7` = 0

⇒ x = 3.5.

So there is only one value of x for which f(x) has extreme value which is x = 3.5.

Therefore, only one extreme value of the given function is possible. (Answer)