Answer:
a) d²y/dx² = ½ x + y − ½
b) Relative minimum
Step-by-step explanation:
a) Take the derivative with respect to x.
dy/dx = ½ x + y − 1
d²y/dx² = ½ + dy/dx
d²y/dx² = ½ + (½ x + y − 1)
d²y/dx² = ½ x + y − ½
b) At (0, 1), the first and second derivatives are:
dy/dx = ½ (0) + (1) − 1
dy/dx = 0
d²y/dx² = ½ (0) + (1) − ½
d²y/dx² = ½
The first derivative is 0, and the second derivative is positive (concave up). Therefore, the point is a relative minimum.
The expression √(128x⁸y³z⁹) is equivalent to the expression 8x⁴yz⁴ √(2yz). Then the correct option is C.
The missing options are given below.
<h3>What is an equivalent expression?</h3>
The equivalent is the expressions that are in different forms but are equal to the same value.
The expression is given below.
⇒ √(128x⁸y³z⁹)
Then the expression is given below.
⇒ √[(64 × 2)(x⁴)²(y²y)(z⁸z)]
⇒ 8x⁴yz⁴ √(2yz)
Then the correct option is C.
More about the equivalent link is given below.
brainly.com/question/889935
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1. 5 in and 1/3 in: Area = 5/3 in^2
2. 5 in and 4/3 in: Area= 20/3 in^2
3. 5/2 in and 4/3 in: Area=10/3 in^2
4. 7/6 in and 6/7 in: Area = 1 in^2
Step-by-step explanation:
<u>1. 5 in and 1/3 in</u>
Here,

<u>2. 5 in and 4/3 in</u>
Here,

<u>3. 5/2 in and 4/3 in</u>

<u>4. 7/6 in and 6/7 in</u>
<u>Let</u>

<u>Hence,</u>
1. 5 in and 1/3 in: Area = 5/3 in^2
2. 5 in and 4/3 in: Area= 20/3 in^2
3. 5/2 in and 4/3 in: Area=10/3 in^2
4. 7/6 in and 6/7 in: Area = 1 in^2
Keywords: Rectangle, Area
Learn more about rectangles at:
#LearnwithBrainly
Answer:
16x^2
Step-by-step explanation:
To find the area of a square, we use the formula
A = s^2 where s is the side length
A = (4x)^2
A = 16x^2