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Popular Functions >

extreme f(x)=(x+1)^2(x-4)^5(x-7)^4

Solution

extreme

Solution

Maximum (- 1, 0), Minimum (\frac{32 - 969}{11}, \frac{- 5.99965 E 14 969 - 1.74164 E 16}{285311670611} - \frac{1024 ( 538920 969 - 18340105 )}{14641} - 2458624), Saddle (4, 0), Maximum (\frac{32 + 969}{11}, \frac{5.99965 E 14 969 - 1.74164 E 16}{285311670611} - \frac{1024 ( - 18340105 - 538920 969 )}{14641} - 2458624), Minimum (7, 0)

Solution steps

f^{'} (x) = (x - 4)^{4} (x - 7)^{3} (x + 1) (11 x^{2} - 64 x + 5)

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < \frac{32 - 969}{11},

Increasing

: \frac{32 - 969}{11} < x < 4,

Increasing

: 4 < x < \frac{32 + 969}{11},

Decreasing

: \frac{32 + 969}{11} < x < 7,

Increasing

: 7 < x < \infty

Plug

x = - 1

into

(x + 1)^{2} (x - 4)^{5} (x - 7)^{4} : 0

Maximum (- 1, 0)

Plug

x = \frac{32 - 969}{11}

into

(x + 1)^{2} (x - 4)^{5} (x - 7)^{4} : \frac{- 5.99965 E 14 969 - 1.74164 E 16}{285311670611} - \frac{1024 ( 538920 969 - 18340105 )}{14641} - 2458624

Minimum (\frac{32 - 969}{11}, \frac{- 5.99965 E 14 969 - 1.74164 E 16}{285311670611} - \frac{1024 ( 538920 969 - 18340105 )}{14641} - 2458624)

Plug

x = 4

into

(x + 1)^{2} (x - 4)^{5} (x - 7)^{4} : 0

Saddle (4, 0)

Plug

x = \frac{32 + 969}{11}

into

(x + 1)^{2} (x - 4)^{5} (x - 7)^{4} : \frac{5.99965 E 14 969 - 1.74164 E 16}{285311670611} - \frac{1024 ( - 18340105 - 538920 969 )}{14641} - 2458624

Maximum (\frac{32 + 969}{11}, \frac{5.99965 E 14 969 - 1.74164 E 16}{285311670611} - \frac{1024 ( - 18340105 - 538920 969 )}{14641} - 2458624)

Plug

x = 7

into

(x + 1)^{2} (x - 4)^{5} (x - 7)^{4} : 0

Minimum (7, 0)

Maximum (- 1, 0), Minimum (\frac{32 - 969}{11}, \frac{- 5.99965 E 14 969 - 1.74164 E 16}{285311670611} - \frac{1024 ( 538920 969 - 18340105 )}{14641} - 2458624), Saddle (4, 0), Maximum (\frac{32 + 969}{11}, \frac{5.99965 E 14 969 - 1.74164 E 16}{285311670611} - \frac{1024 ( - 18340105 - 538920 969 )}{14641} - 2458624), Minimum (7, 0)

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x+1)^2(x-4)^5(x-7)^4 ?
The extreme f(x)=(x+1)^2(x-4)^5(x-7)^4 is