2007-11-23 06:33:54 · 6 answers · asked by nafiseh g 1 in Science & Mathematics ➔ Mathematics
I hate quotients. Rewrite if possible.
f(x) = 4x^-2
f ' (x) = 4 * -2x^-3 = -8x^-3
f ''(x) = -8 * -3x^-4 = 24x^-4 = 24/x^4
f ''(-2) = 24 / (-2) ^ 4
f ''(-2) = 24 / 16 = 3/2
2007-11-23 06:43:50 · answer #1 · answered by ? 3 · 0⤊ 2⤋
f(x)= 4/x^2 = 4 (x^(-2))
use derivative of x^m = m x^(m-1)
in your example m =-2
f '(x) = 4 (-2)x^(-2-1) = -8x^(-3)
f "(x) = -8(-3)x^(-3 -1) = 24 x^(-4) = 24/(x^4)
f "(-2) = 24 /((-2)^4) = 24 /16 = 3/2 = 1.5
2007-11-23 14:41:40 · answer #2 · answered by Any day 6 · 0⤊ 2⤋
f (x) = 4 x^(-2)
f `(x) = (- 8) x^(- 3)
f " (x) = 24 x^(- 4) = 24 / x^4
f "(- 2) = 24/16 = 3/2
2007-11-23 14:47:17 · answer #3 · answered by Como 7 · 2⤊ 1⤋
thats very simple...
first, get the first derivative of your equation, then its 2nd derivative..in your case,
f(x) = 4/(x^2),
f'(x) = ((2x)(4) - 0(x^2))/ (x^2)^2
f'(x) = 8/x^3, then
f"(x) = ((3x^2)(8) - 0(X^3))/(x^3)^2
f"(x) = 24/X^4......2nd derivative!!
substitute the value of x=-2, then
f"(-2) = 24/((-2)^4
therefore,
f"(-2) = 3/2.....ANSWER
2007-11-23 14:53:54 · answer #4 · answered by slow poke 1 · 0⤊ 2⤋
8
The second derivative is just f''(x)=8, so it's 8 wherever you measure it...
Sorry... Didn't see the "/" after the 4. The correct answer must be the next one:
2007-11-23 14:36:57 · answer #5 · answered by artie 4 · 0⤊ 1⤋
f''(x) = (-2)(-3)4/x^4
f''(-2) = 3/2
2007-11-23 14:39:28 · answer #6 · answered by sahsjing 7 · 2⤊ 0⤋