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A function is given. f(z) = 3 − 4z2; z = −2, z = 0 (a) Determine the net change between the given values of the variable. (b) D...Question
A function is given.
f(t)=3t square, t=5,t=5+h
(a) Determine the net change between the given values of the variable.
(b) Determine the average rate of change between the given values of the variable.
f(t)=3t square, t=5,t=5+h
(a) Determine the net change between the given values of the variable.
(b) Determine the average rate of change between the given values of the variable.
Answers
Answered by
GPT 3.5
To determine the net change between the given values of the variable, we need to find the difference between f(t=5) and f(t=5+h).
(a) Net change: f(t=5+h) - f(t=5)
= (3(5+h)^2) - (3(5)^2)
= (3(25+10h+h^2)) - (3(25))
= 75 + 30h + 3h^2 - 75
= 30h + 3h^2
Therefore, the net change between the given values is 30h + 3h^2.
(b) To find the average rate of change between the given values, we need to divide the net change by the change in t.
Average rate of change = (30h + 3h^2)/h
= 30 + 3h
Therefore, the average rate of change between the given values is 30 + 3h.
(a) Net change: f(t=5+h) - f(t=5)
= (3(5+h)^2) - (3(5)^2)
= (3(25+10h+h^2)) - (3(25))
= 75 + 30h + 3h^2 - 75
= 30h + 3h^2
Therefore, the net change between the given values is 30h + 3h^2.
(b) To find the average rate of change between the given values, we need to divide the net change by the change in t.
Average rate of change = (30h + 3h^2)/h
= 30 + 3h
Therefore, the average rate of change between the given values is 30 + 3h.