It is given that a function f(x) = (x^3) + h(x^2) + kx - 4.
(a) If the curve y = f(x) touches the x-axis at (2,0) , find the values of h and k.
(b) Find the maximum and minimum points of the curve y = f(x).
thz a lot
another difficult differentiation
2007-10-21 6:34 am
回答 (1)
2007-10-21 7:02 am
✔ 最佳答案
(a)f'(x) = 3x^2 + 2hx + k
As the curve touches at (2, 0), f ' (2) = 0
3*4 +4h + k = 0
4h+k = -12 ...(1)
Also, The curve passes through (2,0), i.e. 0 = f(2)
8+4h+2k - 4 = 0
2h + k = -2 ...(2)
Solving (1) and (2), h = -5 and k = 8
(b)
f(x) = x^3 -5x^2 + 8x - 4
f'(x) = 3x^2 - 10x + 8 = 0
(x-2)(3x-4) = 0
x = 2 or 4/3
f " (x) = 6x - 10
f "(2) = 12-10 = 2>0
f "(4/3) = 8 - 10 =-2<0
Maximum point = (4/3, f(4/3)) = (4/3, 4/27)
Minimum point = (2,0)
收錄日期: 2021-04-13 18:13:04
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