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 function is shown by the graph below ⇒ 2nd answer
Step-by-step explanation:
<em>To find the right function chose two points from the graph and substitute the x-coordinate of each point in the function to find the y-coordinate, if they are the same with the corresponding y-coordinates of the points, then the function is shown by the graph</em>
From the figure:
The curve passes through points (-2 , 0) and (2 , 2)
∵
∵ x = -2
- Substitute x by -2
∴
∴ ⇒ it is impossible no square root for (-) number
∴ is not the function shown by the graph
∵
∵ x = -2
- Substitute x by -2
∴
∴
∴ f(-2) = 0 ⇒ same as the y-coordinate of x = -2
∵ x = 2
- Substitute x by 2
∴
∴
∴ f(2) = 2 ⇒ same as the y-coordinate of x = 2
∴ The function is shown by the graph below