Question

Find the minimum and maximum of A over a particular interval [0, 6].

A(x) =
The graph of y = f(x) is represented in the figure_
(Use symbolic notation and fractions where needed )
minimum:
maximum:
f(t) dt

Answer 1

The function f(x) is a horizontal line at y = 10 over the interval [0, 6]. The minimum and maximum of A(x), the integral of f(x), are both 60, as the function's value does not change over the interval.

Step-by-step explanation:

Based on the information provided, since the function f(x) is a horizontal line at y = 10 from 0 ≤ x ≤ 20, the calculation of the minimum and maximum of A(x) over the interval [0, 6] involves integrating the function over this interval. Because the function is constant, the integral of f(x) from x = 0 to x = 6 is simply the area of the rectangle formed by the width of the interval (6 - 0) and the height of the function (10).

The area A is calculated by multiplying the width of the interval by the constant value of f(x):

A = height × width = 10 × 6 = 60

Since the function does not change over this interval, A represents both the minimum and maximum value of the integral from x = 0 to x = 6.