1. given that y=x^(5/2)
a.write down an expression for dy/dx,
b.show that,when x=2,the value of dy/dx can be written os form p√2, where p is an integer to be determind.
2.a function is defined by f(x)=2x^3-6x^2-18x+20
a.the coordinates of the stationary points of y=f(x) are given as (m,30)and (n,-34).Find, using calculus, the values of m and n.
b.write down the coordinates of the stationary points of y=f(x+1).
differentiation
2006-12-11 9:04 am
回答 (1)
2006-12-11 10:20 am
✔ 最佳答案
1dy/dx
=(5/2)x^(3/2)
(b)
when x=2
dy/dx
=(5/2)2^(3/2)
=5√2
2(a)
y=f(x)=2x^3-6x^2-18x+20
dy/dx =6x^2-12x-18=6(x^2-2x-3)=6(x-3)(x+1)
let dy/dx =0, x=-1 or 3
when x=-1, y=30
when x=3, y=-34
so m=-1, n=3
b)
if y=f(x+1)
y=2(x+1)^3-6(x+1)^2-18(x+1)+20
dy/dx=6(x+1)^2-12(x+1)-18
let dy/dx=0
then
x+1-3=0 or x+1+1=0
x=2 or x=0
when x=0, y=-2
when x=2, y=-34
the coordinates of the stationary points are
(0,2) (2,-34)
2006-12-11 02:20:26 補充：
last line (0,-2)
收錄日期: 2021-04-12 14:32:05
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