Determine the second-degree Taylor polynomial P_2(x) for the function f(x)=(4x-11)^(3/2) expanded about x=5

Rubi Garner

Rubi Garner

Answered question

2022-10-28

Determine the second-degree Taylor polynomial P 2 ( x ) for the function f ( x ) = ( 4 x 11 ) 3 / 2 expanded about x=5

Answer & Explanation

Milton Hampton

Milton Hampton

Beginner2022-10-29Added 16 answers

Given: f ( x ) = ( 4 x 11 ) 3 / 2 c = 5
The complete Taylor series is given as:
P ( x ) = n = 0 f n ( c ) n ! ( x c ) n
When it is centered abound x=c
So, P 2 ( x ) f 0 ( c ) 0 ! + f 1 ( c ) 1 ! ( x c ) + f ( 2 ) ( c ) 2 ! ( x c ) 2
Puting c=5
P 2 ( x ) = f ( 5 ) + f ( 5 ) ( x 5 ) + f ( 5 ) 2 ! ( x 5 ) 2 Now  f ( x ) = ( 4 x 11 ) 3 / 2 f ( x ) = d ( ( 4 x 1 ) 3 / 2 ) d x f ( x ) = 3 2 × 4 ( 4 x 11 ) 1 2 f ( x ) = 6 ( 4 x 11 ) 1 / 2 f ( x ) = d d x f ( x ) = d d x ( 6 ( 4 x 11 ) 1 2 ) f ( x ) = 12 ( 4 x 1 ) 1 2 f ( 5 ) = 27 f ( 5 ) = 18 f ( 5 ) = 4

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?