Question

Need help solving Tangent Line Error Bound for a first Taylor polynomial

f(x) = e^x
b=0
L(x) = x+1

Interval [-1, 1]

I've tried using the formula ((x-b)^2)/2 * M
M being the second derivative of f(x) and I'm still not getting the correct answer so can someone please explain how you do this?

When I calculated this I got the max error bound to be e/2 and according to my homework that is wrong.

Answer 1

M is the second derivative? Isn't it the Maximum Value of the 2nd Derivative on the interval?

Answer 2

Yes that is correct, when I do that I get the wrong answer according to my homework. I've tried this 4 times and get it wrong every single time.

Answer 3

Really no one can help?

Answer 4

ok, so the 2nd deriv is still e6x hmm
we need the value of x that maximizes this so that would be 1 or -1

Answer 5

Would the value not be e^1 = e?

Answer 6

e^1 > e^-1 and since we're looking for max you want the greater one so I think that makes it e.

Answer 7

Oh, good point

Answer 8

Yeah so M = e. So then when you use the formula ((x-b)^2)/2 *M I get it to equal e/2 for the interval [1, -1] since b = 0.

Answer 9

so e/2 ?

Answer 10

Yeah that's what I get but my online homework is saying that is incorrect. So I'm just really frustrated.

Answer 11

Ok, I'm not sure what it is after

Answer 12

Alright well thanks anyways.

Answer 13

Nw :)

Answer 14

is this shamil -_-

Answer 15

I know this is completely ridiculous, I am really pissed off.

Answer 16

maybe there is an error in the solutions?

Answer 17

Possibly idk I think I'm going to have to email my professor.