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受欢迎的函数 >

extreme f(x)=sin(x)+sin^3(x),-pi<x<pi

解答

极值点

f (x) = sin (x) + sin^{3} (x), - π < x < π

解答

极小值 (- \frac{π}{2}, - 2), 极大值 (\frac{π}{2}, 2)

求解步骤

找到临界点:

x = - \frac{π}{2}, x = \frac{π}{2}

sin (x) + sin^{3} (x), - π < x < π

的定义域

: - π < x < π

Find intervals:

递减

: - π < x < - \frac{π}{2},

递增

: - \frac{π}{2} < x < \frac{π}{2},

递减

: \frac{π}{2} < x < π

将极值点

x = - \frac{π}{2}

代入

sin (x) + sin^{3} (x) \Rightarrow y = - 2

极小值 (- \frac{π}{2}, - 2)

将极值点

x = \frac{π}{2}

代入

sin (x) + sin^{3} (x) \Rightarrow y = 2

极大值 (\frac{π}{2}, 2)

极小值 (- \frac{π}{2}, - 2), 极大值 (\frac{π}{2}, 2)

作图

流行的例子

extreme y=(x-1)^3(x-5)

e x t re m e y = (x - 1)^{3} (x - 5)

extreme f(x)=4x-6

e x t re m e f (x) = 4 x - 6

extreme f(x)=-2/(x^2),0.5<= x<= 2

e x t re m e f (x) = - \frac{2}{x ^{2}}, 0.5 \leq x \leq 2

extreme f(x)=-2/(x^2),0.5<= x<= 5

e x t re m e f (x) = - \frac{2}{x ^{2}}, 0.5 \leq x \leq 5

extreme f(x)=2-3x

e x t re m e f (x) = 2 - 3 x