絆月~cLaSS

1a)  Differentiate  with respect to x the quotient    (x^3) / (x^2) + 1

1b)  Find the rate of increase of y with respect to x ehwn x= (1/3)兀 rad ,given that y= (1/2)sinx.  what is the smallest positive value of x for which the rate of increase is zero?

1c)  For the expression y= 4+7x-(3x^3)  find  dy/dx , (d^2)y / (dx^2)      Hence  find the value of  dy/dx when (d^2)y/dx^2 =9

希望列有步驟....唔該

mejack1324

1a)   Let y = (x^3) / (x^2) + 1  <---可約簡= = '?
          then y = x+1
Differentiate  with respect to x
  dy/dx = 1

1b)  y= (1/2)sinx
Differentiate  with respect to x
dy/dx = 1/2 *[ d (sinx)/ dx]
dy/dx = 1/2 cosx

When  x= (1/3)兀 (您可看做 183/3=60)
dy/dx = 1/2 cos((1/3)兀) = 1/2 * 1/2 = 1/4


the rate of increase is zero . then put dy/dx = 0
dy/dx = 1/2 cosx = 0
1/2 cosx = 0
cosx = 0

for 0<=x <= 2兀 <---( 題目應該有 range 的. 否則幾細都可以)
cosx = 0
x=兀/2

1c)  y= 4+7x-(3x^3)
        dy/dx = 0 + 7 - 9x^2 = 7-9x^2
         d^2y / dx ^2= 0 - 18x = -18x

dy/dx = 7-9x^2
d^2y / dx ^2 = -18x

when (d^2)y/dx^2 =9
-18x=9
x= -1/2

put x = -1/2 into dy/dx = 7-9x^2
dy/dx = 7 - 9(-1/2)^2
= 7 - 9/4
=19/4

希望沒有錯 0.0

。﹏小痺〞

很『長』『細』的答覆

絆月~cLaSS

thx>>>!!!!!!!!!!!!!  答案沒錯!!!!!!!

小輪

小弟都讀過 a maths 我想問下第一題 係  (x^3)/(x^2)+1 定係 (x^3)/((x^2)+1)  ??

mejack1324

不要緊. 照樣做 Differentiation 就可以了.