Question

Exercise:
1. Find the relative extrema of the function f given by f(x) = x3 - 3x + 2.

Answer 1

Answer:

So, start by determining the first derivative of

f

f

′

=

−

3

x

2

−

12

x

−

9

To determine the function's critical points, make

f

′

=

0

and solve for

x

f

′

=

0

f

′

=

−

3

x

2

−

12

x

−

9

=

0

This is equivalent to

−

3

(

x

2

+

4

x

+

3

)

=

0

, or

x

2

+

4

x

+

3

=

0

x

1

,

2

=

−

4

±

√

4

2

−

4

⋅

1

⋅

3

2

=

{

x

1

=

−

3

x

2

=

−

1

sorry keyboard problem