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How do you find the linearization of #f(x) = x^4 + 5x^2# at a=-1?

Answer 1

Ezekiel Alexander

#L(x)=-6x#

#L(x)=f(a)+f'(a)(x-a)#

We're given #a=-1, f(x)=x^4+5x^2,# so

#(x-a)=(x-(-1))=(x+1)#

#f(a)=f(-1)=(-1)^4+5(-1)^2=1+5=6#

#f'(x)=4x^3+10x#

#f'(a)=f'(-1)=4(-1)^3+10(-1)=4-10=-6#

Then,

#L(x)=6-6(x+1)#

#L(x)=6-6x-6#

#L(x)=-6x#

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Answer 2

Axel Alvarez

To find the linearization of ( f(x) = x^4 + 5x^2 ) at ( a = -1 ), follow these steps:

Find the first derivative of ( f(x) ) with respect to ( x ).
Evaluate the derivative at ( x = a ).
Plug the values of ( a ) and ( f(a) ) into the equation for linearization: ( L(x) = f(a) + f'(a)(x - a) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.