Let f(x)=7x2.
Find a value A such that the average rate of change of f(x) from 1 to A equals 84.
A=
4 answers
Its F(x)= 7x^(2). Sorry.
f(1) = 7(1)^2 = 7
f(A) = 7A^2
avg rate of change = (7a^2 - 7)/(a-1)
(7a^2 - 7)/(a-1) = 84
7a^2 - 7 = 84a - 84
7a^2 - 84a + 77 = 0
a^2 - 12a + 11 = 0
(a-11)(a-1) = 0
a = 11 or a = 1, but we have to reject a = 1 or else we would be dividing by zero
A =11
check:
f(11) = 7(121) = 847
f(1) = 7
rate of change = (847-7)/(11-1)
= 840/10 = 84
looks ok
f(A) = 7A^2
avg rate of change = (7a^2 - 7)/(a-1)
(7a^2 - 7)/(a-1) = 84
7a^2 - 7 = 84a - 84
7a^2 - 84a + 77 = 0
a^2 - 12a + 11 = 0
(a-11)(a-1) = 0
a = 11 or a = 1, but we have to reject a = 1 or else we would be dividing by zero
A =11
check:
f(11) = 7(121) = 847
f(1) = 7
rate of change = (847-7)/(11-1)
= 840/10 = 84
looks ok
Thank you very much Reiny. You broke it down perfectly for me.
or, picking up at
(7a^2 - 7)/(a-1) = 84
7(a-1)(a+1) / (a-1) = 84
7(a+1) = 84
a+1 = 12
a = 11
(7a^2 - 7)/(a-1) = 84
7(a-1)(a+1) / (a-1) = 84
7(a+1) = 84
a+1 = 12
a = 11
1 answer