(The function is cubed) How do you find a and b?
#f(x)=3(ax-b/x)^3#
Given #f# #(3/2)# = #3#
and #f'# #(3/2)# = 30
Given
and
2 Answers
Explanation:
Since
we get:
that's
Since
we get
that's
Let's substitute
that's
Since
and we'll substitute it in
The we get:
Since
Please see below.
Explanation:
We are given:
Using the definition of
So
Clear fractions by multiplying by
We are also given some information about the derivative of
we find the derivative:
#f'(x) = 9(ax-b/x)^2(a+b/x^2)#
Using
# = 9(3/2a-2/3b)^2(a+4/9b)#
# = (3/2a-2/3b)^2(9a+4b)#
Recall from above that the first factor is
Solving the system
We get