Find the Linearization at a=1 f(x)=x^4+2x^2 , a=1

Problem

ƒ(x)=x4+2*x2,a=1

Solution

1. Identify the formula for the linearization L(x) of a function ƒ(x) at a point a which is L(x)=ƒ(a)+ƒ(a)′*(x−a)

2. Evaluate the function at the given point a=1 by substituting x=1 into ƒ(x)

ƒ(1)=(1)4+2*(1)2

ƒ(1)=1+2=3

3. Find the derivative of the function ƒ(x) using the power rule.

(d(x4)+2*x2)/d(x)=4*x3+4*x

4. Evaluate the derivative at the point a=1 to find the slope of the tangent line.

ƒ(1)′=4*(1)3+4*(1)

ƒ(1)′=4+4=8

5. Substitute the values ƒ(1)=3 ƒ(1)′=8 and a=1 into the linearization formula.

L(x)=3+8*(x−1)

6. Simplify the expression by distributing the slope and combining like terms.

L(x)=3+8*x−8

L(x)=8*x−5

Final Answer

L(x)=8*x−5

Want more problems? Check here!