Consider the function f ( x ) = − 5 x 3 f(x)=-5x3. Determine the average rate of

The average rate of change in the interval (3, 3.5) is -158.75          

Step-by-step explanation:

We are given the following function in the question:

We have to find average rate of change over the interval:

x = 3 to x = 3.5

Average rate of change  =

Thus, the average rate of change in the interval (3, 3.5) is -158.75

=  -5√7 -(√2)

Step-by-step explanation:

3√7- √7 -2√7+√8 -5√7-3√2

=3√7- √7 -2√7 -5√7+√8 -3√2   (first we place similar radicands together)

=-5√7+√8 -3√2                     ( solve the similar radicands)

=-5√7+√2³ -3 (2^1/2)          ( break 8 into powers of 2)

=-5√7+ (2)^3/2  -3 (2^1/2)        (solve 2 power with the radical sign)

=  -5√7+(2^1/2){ 2-3}             ( taking2^1/2 as common)

=  -5√7+(2^1/2){ -1}                  ( solving the co - efficients of 2^1/2)

=  -5√7 -1 (2^1/2)  

=  -5√7 -(√2)          {answer}