Answer: Please see explanation column for answers. Also check number 6, its question is incomplete. i used an assumed function, incase its not the same function with the one omitted, just follow steps
Step-by-step explanation: Questions 1-5 do not need any step by step explanation, its purely straight forward but Question 6 involves step by step explanation but is not a complete question, though i used an assumed function.
FALSE ---> 1. THE ABSOLUTE MAXIMUM OF A FUNCTION ALWAYS OCCURS WHERE THE DERIVATIVE HAS A CRITICAL FUNCTION. ___TRUE_____-->__ 2. IMPLICIT DIFFERENTIATION CAN BE USED TO FIND dy/dx WHEN x IS DEFINED IN TERMS OF y .
TRUE__--->3. IN A RELATED RATES PROBLEM, THERE CAN BE MORE THAN TWO QUANTITIES THAT VARY WITH TIME.
_FALSE ---> 4. A CONTINUOUS FUNCTION ON AN OPEN INTERVAL DOES NOT HAVE AN ABSOLUTE MAXIMUM OR MINIMUM.
____TRUE__--->____ 5. IN A RELATED RATES PROBLEM, ALL DERIVATIVES ARE WITH RESPECT TO TIME.
6. FIND THE MAXIMUM ABSOLUTE EXTREMUM AS WELL AS ALL VALUES OF x WHERE IT OCCURS ON THE SPECIFIED DOMAIN
----Incomplete question Please.
But assuming the function---- f(x)= x³ -3x+1
for (E)=(0,3)
step 1= let us use the power rule to find derivative of f(x)= x^3 -3x+1
we will have f¹ (x) = 3x² -3
The critical values occurs when 3x² -3 = 0
which makes x=⁺₋1
As can be seen 3x² -3 = 0
3x²=3
x²=3/3=1
x= ⁺₋1
step 2=Now x= -1 cannot be considered because it is not in the interval of the critical values (0,3)
therefore we consider x=1
step 3=The absolute extremes occurs at x=0, x=1, x=3 forf(x)= x³ -3x+1
when x=0, f(0)= 0³-3(0)+ 1= 1
x=1 f(1)=1³-3(1) +1= -1
x=3 f(3)= 3³ -3(3)+1= 19
Absolute minimum at x=1 has absolute value of-1
Absolute maximum of x=3 has absolute value of 19