What is the maximum number of possible extreme values for the function, f(x)=x^3-7x-6

The maximum number of possible extreme values for the function,

is:

2

Step-by-step explanation:

By the Theorem of extreme values of a polynomial function we have:

The graph of a  polynomial equation of degree n has atmost ( less than or equal to) "n-1" extreme values (  i.e. minima and/or maxima).

That means the total number of extreme values could be n-1, n-3, n-5 etc.

Hence, here we have a polynomial equation as:

i.e. we have a polynomial function of degree 3 i.e. n=3

So, the maximum number of possible extreme values that may exits is: 2

( Since n-1=3-1=2)

x² + 3x + 7 = 0       [ax² + bx + c]

a = 1

b = 3

c = 7

quadratic formula:

    (+/- is this ±)

plug in the numbers into the variables

your answer is a