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受欢迎的函数 >

inflection x^4-32x^2+1

解答

拐点

x^{4} - 32 x^{2} + 1

解答

(- \frac{4}{3}, - \frac{1271}{9}), (\frac{4}{3}, - \frac{1271}{9})

求解步骤

f^{''} (x) = 12 x^{2} - 64

Find intervals:

向上凹

: - \infty < x < - \frac{4}{3},

向下凹

: - \frac{4}{3} < x < \frac{4}{3},

向上凹

: \frac{4}{3} < x < \infty

将

x = - \frac{4}{3}

代入

x^{4} - 32 x^{2} + 1 : - \frac{1271}{9}

(- \frac{4}{3}, - \frac{1271}{9})

将

x = \frac{4}{3}

代入

x^{4} - 32 x^{2} + 1 : - \frac{1271}{9}

(\frac{4}{3}, - \frac{1271}{9})

(- \frac{4}{3}, - \frac{1271}{9}), (\frac{4}{3}, - \frac{1271}{9})

作图

流行的例子

slopeintercept 3x-4y=12

s l o p e in t erce pt 3 x - 4 y = 12

slopeintercept (2y+9x)/2 =x+1

s l o p e in t erce pt \frac{2 y + 9 x}{2} = x + 1

求反函数 log_{5}((1-x)/(1+x))

in v erse lo g_{5} (\frac{1 - x}{1 + x})

定义域 f(x)= x/(x+7)

d o main f (x) = \frac{x}{x + 7}

距离 (-1,4),(5,-1)

d i s t an ce (- 1, 4), (5, - 1)