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If f(−1) = −3 and f prime of x equals the quotient of 4 times x squared and the quantity x cubed plus 3 , which of the following is the best approximation for f(–1.1) using local linearization?

–7.2
2.8
–1.2
–3.2

If f1 3 and f prime of x equals the quotient of 4 times x squared and the quantity x cubed plus 3 which of the following is the best approximation for f11 using class=

Respuesta :

Answer:

[tex]-3.2[/tex]

Step-by-step explanation:

Linear approximation formula is

[tex]f(x)=f(a)+f'(a)(x-a)[/tex], the value of x is -1.1 and a is [tex]-1[/tex]

Answer:

-3.2

Step-by-step explanation:

f(-1) = -3

f'(x) = [tex]\frac{4x^{2} }{x^{3} +3}[/tex]

f(-1.1) = ?

f'(-1) = [tex]\frac{4(-1)^{2} }{(-1)^{3}+3 } =2[/tex]

[tex]y-y_{1}=m(x-x_1)\\ y-(-3)=2(x+1)\\y+3=2x+2\\y=2x+2-3\\y=2x-1\\[/tex]

plug in -1.1 into x to get the best approximation

[tex]y=2x-1\\y=2(-1.1)-1\\y=-2.2-1\\y=-3.2\\[/tex]

The best approximation for f(-1.1), using local linearization, is y=-3.2.