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Popular >

inflection f(x)=(x-1)^2(x-2)

Solution

inflection points

f (x) = (x - 1)^{2} (x - 2)

Solution

(\frac{4}{3}, - \frac{2}{27})

Solution steps

f^{''} (x) = 2 (3 x - 4)

Find intervals:

Concave Downward

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

Concave Upward

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

Plug

x = \frac{4}{3}

into

(x - 1)^{2} (x - 2) : - \frac{2}{27}

(\frac{4}{3}, - \frac{2}{27})

Popular Examples

inflection x^4-32x^2+4 inflection points

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

intercepts of (x^2-16)/(2x+8)intercepts

\frac{x ^{2} - 16}{2 x + 8}

midpoint (-1/2 , 7/2),(-2,2)midpoint

(- \frac{1}{2}, \frac{7}{2}), (- 2, 2)

critical f(x)=x^3-6x^2+9x+1 critical points

f (x) = x^{3} - 6 x^{2} + 9 x + 1

distance (1/2 , 1/2),(-2,3)distance

(\frac{1}{2}, \frac{1}{2}), (- 2, 3)

Frequently Asked Questions (FAQ)

What is the inflection f(x)=(x-1)^2(x-2) ?
The inflection f(x)=(x-1)^2(x-2) is (4/3 ,-2/27)