Critical points occur where the gradient is zero. This is guaranteed whenever
and either
or
.
The Hessian matrix for this function looks like
and has determinant
Maxima occur whenever the determinant is positive and
. Minima occur whenever both the determinant and
are positive. Saddle points occur whenever the determinant is negative.
At
, you have a saddle point since the determinant reduces to -324, so
is the saddle point.
At
, the determinant is
and
, so
is a local maximum.
No other critical points remain, so you're done.
Answer:
See below in bold.
Step-by-step explanation:
Mean = 150 cm = 150 * 0.033 feet
= 4.95 feet.
The standard deviation = 10 cm = 10 * 0.033
= 0.33 feet.
Question 1:
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Total points = 100
Total question = 40
Type of questions : 2-points question and 4-points questions
Assumed all 40 questions are 2-points questions.
Total points = 40 x 2 = 80
Difference in points = 100 - 80 = 20 points
Difference in the 2 type of questions = 4 - 2 = 2
Number of 4 marks questions = 20 ÷ 2 = 10
Number of 2 marks questions = 40 - 10 = 30
Answer: There are 10 4-marks questions and 30 2-marks questions.
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Question 2:
------------------------
Let x be the number of offices you need to clean.
Total cost = 315 + 4x
Total revenue = 25x
To break even,
315 + 4x = 25x
21x = 315
x = 15
Answer: You need to clean 15 offices to break even.
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Question 3:
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Total distance (including return trip) = 255 + 255 = 510 miles
Total time taken = 1.7 + 1.5 = 3.2 hours
Speed = Distance ÷ time
Speed = 510 ÷ 3.2 = 159.38 miles/hour
Answer: The average speed is 159.38 miles/hour
Answer:
the correct graph is b for this problem
