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asked in 科學數學 · 9 years ago

請問有關function increasing 的求法?

請問有關 what x values is the function increasing or decreasing 要怎麼求

可以告訴我下列的方程式的答案嗎?

1) f(x)= 13

2) f(x)= -3│x-5│+13

3) f(x)= 3/25 x^2 +3

4) f(x)= 根號x -10

5) f(x)= 127/3960 x^3 +1354/1847 x^2+3241/660 x-10

6) f(x)= x立方根

7) f(x)= 2/243 x^4 - 8/27 x^2 - 6

8) f(x)= 2的x次方

Update:

謝謝你~ 真的太感謝了~

1 Answer

Rating
  • 麻辣
    Lv 7
    9 years ago
    Favorite Answer

    1)f(x)= 13=固定值.不增不減2)f(x)= -3│x-5│+13x≧5 => f(x)=-3(x-5)+13=-3x+28 => 遞減函數x<5 => f(x)=-3(-x+5)+13=3x-2 => 遞增函數3)f(x)=3/25*x^2+3=yy-3=3x^2/5≧0, 拋物線開口向上x≧0, 遞增函數x<0, 遞減函數4)f(x)=√(x-10)=yy^2=x-10≧0 => 拋物線開口向右.y≧0, 遞增函數y<0, 遞減函數5)f(x)=127/3960*x^3+1354/1847*x^2+3241/660*x-10f'(x)=3*127/3960*x^2+2*1354/1847*x+3241/660=0x1=-10.268, x2=-4.971f"(x)=6*127/3960*x+2*1354/1847f"(-10.268)=-0.51<0 => 有極大值f"(-4.971)=0.51<0 => 有極小值所以x<-10.491 => 遞增部份-10.491<=x<-4.971 => 遞減部份x>=-4.971 => 遞增部份6)f(x)=x^(1/3)x≧0, 遞增函數 x<0, 遞減函數7)f(x)=2/243*x^4-8/27*x^2-6f'(x)=16/243*x^3-16/27*x=0 => x=0 or x=+-3f"(x)=48/243*x^2-16/27f"(0)=-16/27<0 => 有極大值f"(+-3)=48*9/243-16/27=(48-16)/27=32/27>0 有極小值x<-3 => 遞減部份-3<=x<0 遞增部份0<=x<3 遞減部份x>=3 遞增部份8)f(x)=2^x => 遞增函數

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