Question

An equation of a function y(t) is shown.

y(t)=−t²+14t−40

Which of the following statements are true about the graph of y(t) for
6≤t≤8 and WHY?

a. The value of y(t) increases over the interval 6≤t≤7

b. The value of y(t) increases over the interval 7≤t≤8

c. The average rate of change over the interval 6≤t≤8 is 0

d. The value of y(t) is constant over the interval 6≤t≤8

e. The average rate of changer over the interval 6≤t≤7 is the same as the average rate of change over the interval 7≤t≤8

Answer 1

From the given function, to explain the correct answer I will plot the graph for :
y(t)=-t^2+14t-40
thus the graph will be as shown in the figure:
From the graph we deduce that the correct statement is:
y'(t)=-2t+14=0
thus
t=7
thus
y(7)=0
thus the correct statement is:
c. The average rate of change over the interval 6≤t≤8 is 0