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受欢迎的函数 >

extreme f(x)=((-8x^3+3x^2))/4

解答

极值点

f (x) = \frac{( - 8 x ^{3} + 3 x ^{2} )}{4}

解答

极小值 (0, 0), 极大值 (\frac{1}{4}, \frac{1}{64})

求解步骤

f^{'} (x) = \frac{3 x ( - 4 x + 1 )}{2}

Find intervals:

递减

: - \infty < x < 0,

递增

: 0 < x < \frac{1}{4},

递减

: \frac{1}{4} < x < \infty

将

x = 0

代入

\frac{- 8 x ^{3} + 3 x ^{2}}{4} : 0

极小值 (0, 0)

将

x = \frac{1}{4}

代入

\frac{- 8 x ^{3} + 3 x ^{2}}{4} : \frac{1}{64}

极大值 (\frac{1}{4}, \frac{1}{64})

极小值 (0, 0), 极大值 (\frac{1}{4}, \frac{1}{64})

作图

流行的例子

extreme f(x)=2x^3+x^2-4x+4

e x t re m e f (x) = 2 x^{3} + x^{2} - 4 x + 4

extreme f(x,y)=y(e^x-1)

e x t re m e f (x, y) = y (e^{x} - 1)

extreme f(x)= x/(x^2+9),-4<= x<= 5

e x t re m e f (x) = \frac{x}{x ^{2} + 9}, - 4 \leq x \leq 5

extreme x^3+3x^2-24x

e x t re m e x^{3} + 3 x^{2} - 24 x

extreme-x^3+4xy-2y^2+1

e x t re m e - x^{3} + 4 x y - 2 y^{2} + 1