Question

Find the linearization of f(x) = x^3 + x at a = 2, and then use it to estimate f(2.2).

Answer 1

take derivative of x^3+x

Answer 2

3x^2+1?

Answer 3

good.
L(x)=f(x)+f'(x)dx
f(x)=x^3+x
f'(x)=3x^2+1

Answer 4

evaluate at 2

Answer 5

37?

Answer 6

I think that's wrong :/ Ughh. Im so dumb

Answer 7

f'(2)=4
f(2)=2^3+2=10
dx=0.2 because we want to estimate 0.2( 2.2-2)
f(2.2)=10+4(0.2)

Answer 8

then we add them?

Answer 9

10+4(0.2)=10.8

Answer 10

Its telling me the answer has to be between 12 and 14 :?

Answer 11

f'(2)=13 (arithmethic error above)
f(2)=2^3+13(.2)=10
dx=0.2 because we want to estimate 0.2( 2.2-2)
f(2.2)=10+13(0.2)=12.6

Answer 12

what went wrong though? I cant find the error..

Answer 13

and thanks :) that answer is correct but what was wrong in our old answer?

Answer 14

plugging in 2 into 3x^2+1, I got 4 instead of correct answer of 13; silly arithmetic error