Question

Let f be the function defined by f(x)=sec x+csc x. Which of the following expressions is the average rate of change of fover the interval [ π /4 , 3π /8 ] ？ A frac f( 3π /8 )+f( π /4 )2 B frac f( 3π /8 )+f( π /4 ) 3π /8 + π /4 C frac f( 3π /8 )-f( π /4 ) 3π /8 - π /4 D f( 3π /8 )-f( π /4 )

Answer 1

To find the average rate of change of the function f(x) = sec(x) + csc(x) over the interval [π/4 , 3π/8], we use the formula: Average Rate of Change = (f(b) - f(a))/(b - a).

Step-by-step explanation:

The average rate of change of a function f over an interval [a, b] is given by the formula:
Average Rate of Change = (f(b) - f(a))/(b - a).

In this case, f(x) = sec(x) + csc(x). To find the average rate of change over the interval [π/4 , 3π/8], we substitute π/4 for a and 3π/8 for b in the formula and calculate:

Average Rate of Change = (f(3π/8) - f(π/4))/(3π/8 - π/4).

By simplifying the expression, we find the average rate of change of f over the given interval. The average rate of change of the function f(x) = sec x + csc x over the interval [π /4 , 3π /8] is calculated using the formula ∆f / ∆x, which is the difference in the function values divided by the difference in the x-values. In mathematical terms, it is (f(3π /8) - f(π /4)) / (3π /8 - π /4). Hence, the correct answer is C.