MATH 1325 – EXAM 4 NAME: ______________________________ SHOW ALL WORK. ANSWERS WITHOUT WORK WILL RECEIVE NO CREDIT. YOU MUST USE A PENCIL. READ ALL DIRECTIONS. POINTS WILL BE DEDUCTED FOR FAILURE TO FOLLOW DIRECTIONS. TRUE/FALSE – WRITE THE WORD THAT BEST DESCRIBES THE GIVEN STATEMENT BY WRITING EITHER "TRUE" OR "FALSE" IN THE SPACE PROVIDED TO THE LEFT OF THE PROBLEM. __________ 1. THE ABSOLUTE MAXIMUM OF A FUNCTION ALWAYS OCCURS WHERE THE DERIVATIVE HAS A CRITICAL FUNCTION. __________ 2. IMPLICIT DIFFERENTIATION CAN BE USED TO FIND dy dx WHEN x IS DEFINED IN TERMS OF y . __________ 3. IN A RELATED RATES PROBLEM, THERE CAN BE MORE THAN TWO QUANTITIES THAT VARY WITH TIME. __________ 4. A CONTINUOUS FUNCTION ON AN OPEN INTERVAL DOES NOT HAVE AN ABSOLUTE MAXIMUM OR MINIMUM. __________ 5. IN A RELATED RATES PROBLEM, ALL DERIVATIVES ARE WITH RESPECT TO TIME. MULTIPLE CHOICE – CHOOSE THE ONE ALTERNATIVE THAT BEST COMPLETES THE STATEMENT OR ANSWERS THE QUESTION BY CIRCLING THE CORRECT LETTER. 6. FIND THE MAXIMUM ABSOLUTE EXTREMUM AS WELL AS ALL VALUES OF x WHERE IT OCCURS ON THE SPECIFIED DOMAIN
Answers
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
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The domain of the function is the set of all values x such that x is greater than or equal to one-quarter.
The range of the function is all real numbers.
The vertex of the function is (one-quarter, negative 6 and one-eighth).
The function has two x-intercepts.
The function is increasing over the interval (negative 6 and one-eighth, ∞).
Answers
The statements true about the the function f(x) = 2x2 – x – 6 are-
- The vertex of the function is (one-quarter, negative 6 and one-eighth).
- The function has two x-intercepts.
What is vertex of parabola?
The vertex of parabola is the point at the intersection of parabola and its line of symmetry.
Now the given function is,
f(x) = 2x^2 – x – 6
Also, it is given that the vertex is located at (0.25, -6) and the parabola opens up, the function has two x-intercepts.
Comparing the given function with standard form,
f(x) = a x^2 bx + c
By comprison we get,
a = 2
b = -1
c = -6
Now, x-coordinate of vertex is given as,
x = -b/2a
put the values we get,
x = -(-1)/2*2
or, x = 1/4
Put the value of x in given function, so y-coordinate of the vertex is given as,
f(1/4) = 2(1/4)² - 1/4 - 6
= -49/6
= -6 1/8
Hence, The statements true about the the function f(x) = 2x2 – x – 6 are-
- The vertex of the function is (one-quarter, negative 6 and one-eighth).
- The function has two x-intercepts.
More about vertex :
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Answer:
The vertex of the function is (one-quarter, negative 6 and one-eighth).
The function has two x-intercepts.
Step-by-step explanation:
The answer above is correct.
Answers
Given:
Endpoints of a line segment AB are A(2,3) and B(8,11).
To find:
(1) Slope of AB.
(2) Length of AB.
(3) Midpoint of AB.
(4) Slope of a line perpendicular to AB.
Solution:
We have, endpoints of line segment AB, A(2,3) and B(8,11).
(1)
Slope of AB is
Therefore, the slope of AB is .
(2)
Length of AB is
Therefore, the length of AB is 10 units.
(3) Midpoint of AB is
Therefore, the midpoint of AB is (5,7).
(4)
Product of slopes of two perpendicular lines is -1.
Let the slope of line perpendicular to AB be m₁.
So, slope of line perpendicular to AB is .
Answers
Answer:- 8
Step-by-step explanation:
-4 + 4(3)/ -4+3
-4 +12 / -1
8/-1
Answers
Answer:
0.7385 = 73.85% probability that it is indeed a sample of copied work.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Identified as a copy
Event B: Is a copy
Probability of being identified as a copy:
80% of 15%(copy)
100 - 95 = 5% of 100 - 15 = 85%(not a copy). So
Probability of being identified as a copy and being a copy.
80% of 15%. So
What is the probability that it is indeed a sample of copied work?
0.7385 = 73.85% probability that it is indeed a sample of copied work.
Answers
The solution to the equation is m = 400
What are equations
- Equations are used to expressed quantities that are of equal values.
- Equations are identified by the "=" sign
The equation is given as:
Rewrite the above equation as
Divide 2400 by 6
Hence, the solution to the equation is m = 400
See attachment for the bar diagram
Read more about equations at:
What are the coordinates of point B?
Answers
Answer: the coordinates are (3,-7)
Step-by-step explanation: just took the khan academy quiz! hope you do well loves <3
Final answer:
To find the coordinates of point B, we first apply the midpoint formula, with point M as the midpoint and point A given. Solving for point B's coordinates we find they are (3, -7).
Explanation:
In order to find the coordinates of point B, we need to use the midpoint formula. The midpoint M of two points A (x1, y1) and B (x2, y2) is given as:
M = [(x1 + x2)/2 , (y1 + y2)/2].
Given that the midpoint M is (-1.5, -1) and point A is (-6,5), we can use the midpoint formula to calculate the coordinates of point B by rearranging the formula to solve for x2 and y2 (the coordinates of point B):
x2 = 2*xm - x1, y2 = 2*ym - y1.
Plugging in known values, the x-coordinate of point B (x2) = 2*-1.5 - (-6) = 3 and the y-coordinate of point B (y2) = 2*-1 - 5 = -7.
So, the coordinates of point B are (3, -7).
Learn more about Midpoint Formula here:
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