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
