Each of these extreme value problems has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. ln(x^2+1)
Answers
Answer:
The minimum value of the given function is f(0) = 0
Step-by-step explanation:
Explanation:-
Extreme value :- f(a, b) is said to be an extreme value of given function 'f' , if it is a maximum or minimum value.
i) the necessary and sufficient condition for f(x) to have a maximum or minimum at given point.
ii) find first derivative and equating zero
iii) solve and find 'x' values
iv) Find second derivative then find the minimum value at x=a
v) Find second derivative then find the maximum value at x=a
Problem:-
Given function is f(x) = log ( x^2 +1)
step1:- find first derivative and equating zero
……………(1)
the point is x=0
step2:-
Again differentiating with respective to 'x', we get
on simplification , we get
put x= 0 we get > 0
then find the minimum value at x=0
Final answer:-
The minimum value of the given function is f(0) = 0
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Graph the image of the given triangle after the transformation that has the rule (x, y)→(−x, −y)
Answers
Answer:
Step-by-step explanation: do you have a graph?
Answers
The perimeter of the quadrilateral is 4z 16.
What is Perimeter?
To calculate the perimeter, or distance around the rectangle, sum all four side lengths. This may be done quickly by adding the length and breadth and then multiplying the total by two because each side length has two lengths. The perimeter formula is perimeter=(length+width)2.
The 4 sides of quadrilateral is z-4.
Now, the Perimeter of quadrilateral
= (z-4) + (z-4) + (z-4) + (z-4)
= 4 (z-4)
= 4z- 16
Thus, the perimeter is 4z- 16.
Learn more about Perimeter here:
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Answer:
4z-16 units
Step-by-step explanation:
The perimeter of the rectangle is 4z-16 units.
Answers
Answer:
i think 15
Step-by-step explanation:
15
Answers
Answer:
0.11
Step-by-step explanation:
The events are independent, so:
P(A and B) = P(A) × P(B)
P = 0.5 × 0.22
P = 0.11
Answers
Step-by-step explanation:
∑⁴ₙ₌₁ -144 (½)ⁿ⁻¹
This is a finite geometric series with n = 4, a₁ = -144, and r = ½.
S = a₁ (1 − rⁿ) / (1 − r)
S = -144 (1 − (½)⁴) / (1 − ½)
S = -270
If you wanted to find the infinite sum (n = ∞):
S = a₁ / (1 − r)
S = -144 / (1 − ½)
S = -288
Answer:
It's A: -288
Step-by-step explanation:
on edge 2021
(B) What is the least squares regression line
(C) According to the model in (b), for every increase of $1000 in income, the ulcer rate (per 100 population) will go down by _________ points.
Answers
Answer:
B) y = -9.98×10⁻⁵ x + 13.95
C) 0.1
Step-by-step explanation:
Using Excel, the least squares regression line, rounded to two decimal places, is y = -9.98×10⁻⁵ x + 13.95.
The slope is -9.98×10⁻⁵, so if x increases by 1000, then y changes by -9.98×10⁻² = -0.0998. Rounded to one decimal place, the ulcer rate per 100 population will go down by 0.1 points.