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). Hence sketch the curve.
(c) From the graph , find the range of real values of the constant c if
(i) f(x) = c has one real root only.
(ii) f(x) = c has two unequal real roots only.
(iii) f(x) = c has three unequal real roots.
very difficult differentiation~~urgent ...
2007-10-21 7:54 pm
回答 (1)
2007-10-21 11:24 pm
✔ 最佳答案
a)h=-5,k=8b)f(x) = x^3 -5x^2+ 8x - 4
minimum point is(2,0)
maximum point is (4/3,4/27)
(c)after you sketch the graph
you add a straight line y=c to solve the above situation
(i)
from the result(b),c<0 or c>4/27,c has one real root only
(ii)
c=0 or c=4/27,c has two unequal real roots only
(iii)
0<4/27,c has three unequal real roots.
2007-10-21 15:28:50 補充：
(iii)0 is less than c,c is less than 4/27
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