Question

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

Answer 1

-3.2

Explanation:

f(-1) = -3

f'(x) =
`(4x^(2) )/(x^(3) +3)`

f(-1.1) = ?

f'(-1) =
`(4(-1)^(2) )/((-1)^(3)+3 ) =2`

`y-y_(1)=m(x-x_1)\\ y-(-3)=2(x+1)\\y+3=2x+2\\y=2x+2-3\\y=2x-1\\`

plug in -1.1 into x to get the best approximation

`y=2x-1\\y=2(-1.1)-1\\y=-2.2-1\\y=-3.2\\`

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

Answer 2

`-3.2`

Explanation:

Linear approximation formula is

`f(x)=f(a)+f'(a)(x-a)`, the value of x is -1.1 and a is
`-1`