Question

Given f′′′(x)=e^x with f′′(0)=7, f′(0)=5,
then f(x)= _______+c

Answer 1

f''(x)=e^x+D
f''(0)=e^(0)+D=7
1+D=7=> D=6
so we have f''(x)=e^x+7
f'(x)=e^x+7x+A
f'(0)=e^(0)+7(0)+A=5
1+0+A=5=>A=4
so we have f'(x)=e^x+7x+4
f(x)=e^x+7x^2/2+4x+C

Answer 2

I believe that the coefficient of the x^2 term should be 3, not 7/2.
f(x) = e^x + 3 x^2 + 4 x + c
Derivative of (e^x + 3 x^2 + 4 x + c) = e^x + 6 x + 4
When x = 0, 1 + 0 + 4 = 5
The second derivative of f(x) is e^x + 6
When x = 0, 1 + 6 = 7
The third derivative of f(x) is e^x

Answer 3

yea i got D=6 and for some reason i write 7
if they alittle about what they are doing then the will see that i had D=6
and accidently replaced it with 7

Answer 4

I will be 77 years old in August and cannot integrate x with pencil and paper. Once knew the basic rules in the 50's, but not today. Therefore, I rely on Mathematica to do the clerical work, an activity viewed by some as sort of, cheating.

Look, the only reason I wrote the last sentence was to respond to a possible veiled insinuation that "if they alittle about what they are doing then the will see that i had D=6 and accidently replaced it with 7", where the word "they" in your mind could and should be replaced with the word "you".

You might be interested in the following video: "Teaching kids real math with computers: Conrad Wolfram on TED.com"

http://blog.ted.com/2010/11/15/teaching-kids-real-math-with-computers-conrad-wolfram-on-ted-com/

Answer 5

i was just saying a may a little typ-o and it is an obvious typ-o
anyone should be able to see 6 does not equal 7