What is the average rate of change of the function #f(z) = 2-5(z^2)# on the interval [-7,2]?

(Yes, that is the same as the slope of the line through the endpoints on the graph.)

So, for this question the answer is

Do the arithmetic.

To find the average rate of change of the function ( f(z) = 2 - 5z^2 ) on the interval ([-7,2]), we use the formula:

[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} ]

where ( f(b) ) is the value of the function at the upper limit of the interval (( b )), ( f(a) ) is the value of the function at the lower limit of the interval (( a )), and ( b - a ) is the length of the interval.

Substituting the values into the formula:

[ f(-7) = 2 - 5(-7)^2 = 2 - 5(49) = 2 - 245 = -243 ] [ f(2) = 2 - 5(2)^2 = 2 - 5(4) = 2 - 20 = -18 ]

So, the average rate of change of ( f(z) ) on the interval ([-7,2]) is:

[ \frac{-18 - (-243)}{2 - (-7)} = \frac{-18 + 243}{2 + 7} = \frac{225}{9} = 25 ]