How to find the linearization at a=1 of f(x) = x^4 + 4x^2?

nyungu6f5

nyungu6f5

Answered question

2023-03-01

How to find the linearization at a=1 of f ( x ) = x 4 + 4 x 2 ?

Answer & Explanation

Julissa Heath

Julissa Heath

Beginner2023-03-02Added 3 answers

The linearization of f ( x ) = x 4 + 4 x 2 at a = 1 is one form of the equation of the line tangent to the graph of f at the point ( 1 , f ( 1 ) )
For f ( x ) = x 4 + 4 x 2 , we have f ( 1 ) = 5 and f ( x ) = 4 x 3 + 8 x , so f ( 1 ) = 12
The tangent line has point-slope form:
y - f ( 1 ) = f ( 1 ) ( x - 1 ) y - 5 = 12 ( x - 1 )
The linearization is:
y = f ( 1 ) + f ( 1 ) ( x - 1 ) y = 5 + 12 ( x - 1 )

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?