Question

find the average rate of change of ( k(x) = -14x^5 ) over the interval 0, 1. write your answer as an integer, fraction, or decimal rounded to the nearest tenth. simplify any fractions.

Explanation:

Step1: Recall the average rate of change formula

The average rate of change of a function \( k(x) \) over the interval \([a, b]\) is given by \(\frac{k(b) - k(a)}{b - a}\). Here, \( a = 0 \), \( b = 1 \), and \( k(x)=- 14x^{5}\).

Step2: Calculate \( k(0) \) and \( k(1) \)

• For \( x = 0 \): \( k(0)=-14(0)^{5}=0 \)
• For \( x = 1 \): \( k(1)=-14(1)^{5}=-14 \)

Step3: Apply the average rate of change formula

Substitute \( a = 0 \), \( b = 1 \), \( k(0) = 0 \), and \( k(1)=-14 \) into the formula:
\[
\frac{k(1)-k(0)}{1 - 0}=\frac{-14 - 0}{1}=-14
\]

Answer:

\(-14\)