Let f(x) = (x − 3)^−2. Find all values of c in (2, 5) such that f(5) − f(2) = f '(c)(5 − 2).?
回答 (4)
2019-03-20 10:12 am
f(x) = (x - 3)⁻²
f '(x) = -2 (x - 3)⁻³
f '(c) = -2 (c - 3)⁻³
f(5) = (5 - 3)⁻² = 1/4
f(2) = (2 - 3)⁻² = 1
f(5) − f(2) = f '(c) (5 − 2)
(1/4) - 1 = -2 (c - 3)⁻³ (3)
-6 (c - 3)⁻³ = -3/4
(c - 3)⁻³ = 1/8
(c - 3)³ = 8
(c - 3)³ = 2³
c - 3 = 2
c = 5
As 5 is not in (2, 5).
Hence, no value of c is found.
(If c is in [2, 5], the answer is c = 5.)
f '(x) = -2 (x - 3)⁻³
f '(c) = -2 (c - 3)⁻³
f(5) = (5 - 3)⁻² = 1/4
f(2) = (2 - 3)⁻² = 1
f(5) − f(2) = f '(c) (5 − 2)
(1/4) - 1 = -2 (c - 3)⁻³ (3)
-6 (c - 3)⁻³ = -3/4
(c - 3)⁻³ = 1/8
(c - 3)³ = 8
(c - 3)³ = 2³
c - 3 = 2
c = 5
As 5 is not in (2, 5).
Hence, no value of c is found.
(If c is in [2, 5], the answer is c = 5.)
2019-03-22 6:33 pm
f(x) = (x - 3)¯²
f(5) = (5 - 3)² = 4
f(2) = (2 - 3)² = 1
f’(x) = f(5) - f(2) / 5-2
f’(x) = -2(x - 3)¯³(1)
-2(x - 3)¯³ = 4 - 1/5 - 2
-2/(x - 3)³ = 3/3 = 1 → (x - 3)³ = -2
(c - 3)³ = -2
-(3 - c)³ = -2
3 - c = 8
-c = 8 - 3
c = -5
there is no ‘c’ in the (2, 5).
f(5) = (5 - 3)² = 4
f(2) = (2 - 3)² = 1
f’(x) = f(5) - f(2) / 5-2
f’(x) = -2(x - 3)¯³(1)
-2(x - 3)¯³ = 4 - 1/5 - 2
-2/(x - 3)³ = 3/3 = 1 → (x - 3)³ = -2
(c - 3)³ = -2
-(3 - c)³ = -2
3 - c = 8
-c = 8 - 3
c = -5
there is no ‘c’ in the (2, 5).
2019-03-20 10:19 am
f(5) = 1/4. f(2) = 1.
We seek "c" such that
-3/4 = f'(c)(3) =>
f'(c) = -1/4.
f'(x) = -2/(x-3)^3. If this is -1/4, then
1/4 = 2/(x-3)^3 =>
(x-3)^3 = 8 =>
x = 5.
So there is no "c" in the open interval (2,5) that satisfies the conditions. And that's not surprising, because f(x) is NOT continuous in the interval (2,5).
We seek "c" such that
-3/4 = f'(c)(3) =>
f'(c) = -1/4.
f'(x) = -2/(x-3)^3. If this is -1/4, then
1/4 = 2/(x-3)^3 =>
(x-3)^3 = 8 =>
x = 5.
So there is no "c" in the open interval (2,5) that satisfies the conditions. And that's not surprising, because f(x) is NOT continuous in the interval (2,5).
2019-03-20 10:12 am
f(5) = 1/4
f(2) = 1 .... m = [1/4 - 1]/[5 - 2]
m = -3/4 / 3 = -1/4
=============== =
f' = (-2)(x - 3)^-3
f'(c) = (-2)(c - 3)^-3 = -1/4
(c - 3)^-3 = 1/8
(c - 3)^3 = 8
c - 3 = 2
c = 5 <<< answer
f(2) = 1 .... m = [1/4 - 1]/[5 - 2]
m = -3/4 / 3 = -1/4
=============== =
f' = (-2)(x - 3)^-3
f'(c) = (-2)(c - 3)^-3 = -1/4
(c - 3)^-3 = 1/8
(c - 3)^3 = 8
c - 3 = 2
c = 5 <<< answer
收錄日期: 2021-05-01 22:33:29
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20190320015723AABm93Q