What is the vertex of a parabola defined by the equation x = 5y2?
1 answer:
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
You might be interested in
Answer:
Step-by-step explanation:
Given
One-eighth times three-elevenths
Required
Solve
One-eighth means 1/8
Three-elevenths means 3/11
So, mathematically; the above expression is represented as thus:
To solve this, we simply multiply the numerator and the denominator together.
After multiplying these together, the next is to check if the resulting can be simplified
If yes,we simplify it and if otherwise, we live it like that.
So,
At this point, the fraction can't be simplified any further.
Hence,
Answer:
Step-by-step explanation:
We are given
Calculation of P+Q:
now, we can combine like terms
Calculation of Q-P:
Firstly, we will distribute negative sign
now, we can combine like terms