Answer:
0.25ab
Step-by-step explanation:
Data provided in the question:
f(x) = xa(1−x)b, 0≤x≤1
or
f(x) = ab(x−x²)
for point of maxima and minima put f'(x) = 0
Thus,
f'(x) = ab(1 - 2x) = 0
or
1 - 2x = 0
or
x = = 0.5
Now,
to check the condition of maxima or minima
f''(x) = ab(0 - 2) = -2ab
since,
f''(x) < 0
therefore,
x = 0.5 is point of maxima
and the maximum value at x = 0.5 of the function is
f(0.5) = ab(0.5 - 0.5²)
= ab(0.25)
= 0.25ab
Answer:
The true statements:
The only value that is in the domains of both functions is 0.
The range of g(x) is all values less than or equal to 0.
==================================
Step-by-step explanation:
See the attached figure:
As shown: f(x) = √x with blue color
When f(x) is reflected across the x-axis the result will be (-√x) with red color.
Then the is reflected result across the y-axis to create the graph of function g(x) = -√(-x) with green color.
<u>Domain </u>of f(x) = [0,∞) & <u>Range</u> of f(x) = [0,∞)
<u>Domain </u>of g(x) = (-∞,0] & <u>Range </u>of g(x) = (-∞,0]
So, according to previous, we will check the statements:
1) The functions have the same range. <u>(Wrong)</u>
2) The functions have the same domains. <u>(Wrong)</u>
3) The only value that is in the domains of both functions is 0. <u>(True)</u>
4) There are no values that are in the ranges of both functions. <u>(Wrong)</u>
5) The domain of g(x) is all values greater than or equal to 0. <u>(Wrong)</u>
6) The range of g(x) is all values less than or equal to 0. <u>(True)</u>
