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Popular >

extreme y=x^3-9x^2+7x-6

Solution

extreme points

y = x^{3} - 9 x^{2} + 7 x - 6

Solution

Maximum (\frac{9 - 2 15}{3}, \frac{972 - 244 15}{9} + 3615 - 147), Minimum (\frac{9 + 2 15}{3}, \frac{972 + 244 15}{9} - 147 - 3615)

Solution steps

f^{'} (x) = 3 x^{2} - 18 x + 7

Find intervals:

Increasing

: - \infty < x < - \frac{2 5}{3} + 3,

Decreasing

: - \frac{2 5}{3} + 3 < x < \frac{2 5}{3} + 3,

Increasing

: \frac{2 5}{3} + 3 < x < \infty

Plug

x = \frac{9 - 2 15}{3}

into

x^{3} - 9 x^{2} + 7 x - 6 : \frac{972 - 244 15}{9} + 3615 - 147

Maximum (\frac{9 - 2 15}{3}, \frac{972 - 244 15}{9} + 3615 - 147)

Plug

x = \frac{9 + 2 15}{3}

into

x^{3} - 9 x^{2} + 7 x - 6 : \frac{972 + 244 15}{9} - 147 - 3615

Minimum (\frac{9 + 2 15}{3}, \frac{972 + 244 15}{9} - 147 - 3615)

Maximum (\frac{9 - 2 15}{3}, \frac{972 - 244 15}{9} + 3615 - 147), Minimum (\frac{9 + 2 15}{3}, \frac{972 + 244 15}{9} - 147 - 3615)

Graph

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Frequently Asked Questions (FAQ)

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