Find the critical points of f(y):Compute the critical points of -5 y^2
To find all critical points, first compute f'(y):( d)/( dy)(-5 y^2) = -10 y:f'(y) = -10 y
Solving -10 y = 0 yields y = 0:y = 0
f'(y) exists everywhere:-10 y exists everywhere
The only critical point of -5 y^2 is at y = 0:y = 0
The domain of -5 y^2 is R:The endpoints of R are y = -∞ and ∞
Evaluate -5 y^2 at y = -∞, 0 and ∞:The open endpoints of the domain are marked in grayy | f(y)-∞ | -∞0 | 0∞ | -∞
The largest value corresponds to a global maximum, and the smallest value corresponds to a global minimum:The open endpoints of the domain are marked in grayy | f(y) | extrema type-∞ | -∞ | global min0 | 0 | global max∞ | -∞ | global min
Remove the points y = -∞ and ∞ from the tableThese cannot be global extrema, as the value of f(y) here is never achieved:y | f(y) | extrema type0 | 0 | global max
f(y) = -5 y^2 has one global maximum:Answer: f(y) has a global maximum at y = 0
Answer:
i. LM || NO (converse alternate interior angle theorem)
ii. <1 ≅ <2 (alternate interior angle theorem)
Step-by-step explanation:
Two or more lines are said to be parallel if they do not meet when extended, even till infinity.
Alternate angles are said to be equal in measure.
Given that;
<1 ≅ < 3,
Since <2 ≅ <3 (alternate interior angle theorem)
Then,
<1 ≅ <2 (transitive property)
Also,
<1 ≅ <2 (alternate interior angle theorem)
Therefore since <1 ≅ <2, thus;
LM || NO (converse alternate interior angle theorem)
1/
V=44.312 in^3
2/
V=42.453 in^3
3/
V=75.36 in^3
4/
V=696.557 in^3
5/
V=671.175 in^3. Hope it help!
Answer:
x^2 - 2x - 12 with remainder 12
Step-by-step explanation:
Synthetic division is the fastest way in which to carry out this division.
The divisor (x - 1) from long division corresponds to the divisor 1 in synthetic division. Setting up synthetic division, we get:
1 / 1 -3 -10 24
1 -2 -12
--------------------------------
1 -2 -12 12
The first three digits {1, -2, -12} are the coefficients of the quotient, and 12 represents the remainder:
The quotient is 1x^2 - 2x - 12 and the remainder is 12.
