Answer:
<em>given function has 2 minimums</em> -
and
Step-by-step explanation:
<u><em>Step 1.</em></u> g'(x) = 4x³ - 10x
<u><em>Step 2.</em></u> Find find the critical points:
4x³ - 10x = 2x(2x² - 5) = 0
= -
,
= 0 ,
=
<u><em>Step 3.</em></u> g'(x) > 0 : -
< x < 0 or x >
g'(x) < 0 : x < -
or 0 < x <
<u><em>Step 4.</em></u>
If x ∈ ( - ∞ , -
) , g(x) is decreasing ;
If x = -
, g(x) has <em>minimum</em> value ;
If x ∈ ( -
, 0 ) , g(x) is increasing ;
If x = 0 , g(x) has maximum value ;
If x ∈ ( 0 ,
) , g(x) is decreasing ;
If x =
, g(x) has <em>minimum</em> value ;
If x ∈ (
, ∞ ) , g(x) is increasing .
⇒ at ( -
, -
) and at (
,
) , g(x) reaches its minimum