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Find the linearization $L(x)$ of the function at $a$$f(x)=x^{4}+3 x^{2}, \quad a=-1$

$L(x)=4+(-2)(x-a)=4-10(x+1)=-10 x-6$

Calculus 1 / AB

Chapter 3

Derivatives

Section 8

Linear Approximations and Taylor Polynomials

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this question asked us to find the linear or ization of the function. What we know we have is X to the fourth plus three x squared. We know that a is negative one. Therefore, plug in negative one for axe and we get four now. Take the derivative of X to the fourth poster X squared for X cubed, plus three times to a sex acts and then do the same thing four times Negative one cubed post, six times negative one. We're plugging in excess negative one. We got negative 10. So the linear or ization is going to be all of acts is four plus negative, too. Times X minus A, which is equivalent to negative 10 x minus six.

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