What is the extreme f(x)=(x-4)^4(x+3)^3 ?

The extreme f(x)=(x-4)^4(x+3)^3 is Saddle(-3,0),Maximum(0,6912),Minimum(4,0)

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extreme f(x)=(x-4)^4(x+3)^3

extreme points

f (x) = (x - 4)^{4} (x + 3)^{3}

Saddle (- 3, 0), Maximum (0, 6912), Minimum (4, 0)

Solution steps

f^{'} (x) = 7 x (x - 4)^{3} (x + 3)^{2}

Find intervals:

Increasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Decreasing

: 0 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = - 3

into

(x - 4)^{4} (x + 3)^{3} : 0

Saddle (- 3, 0)

Plug

x = 0

into

(x - 4)^{4} (x + 3)^{3} : 6912

Maximum (0, 6912)

Plug

x = 4

into

(x - 4)^{4} (x + 3)^{3} : 0

Minimum (4, 0)

Saddle (- 3, 0), Maximum (0, 6912), Minimum (4, 0)

f (x) = 2 x^{3} - 6 x^{2} - 48 x + 10

f (x) = e^{6 x} + e^{- x}

f (x) = \frac{x}{1 + x}

f (x) = x^{2} x + 5

f (x) = \frac{5}{x - 1}

What is the extreme f(x)=(x-4)^4(x+3)^3 ?
The extreme f(x)=(x-4)^4(x+3)^3 is Saddle(-3,0),Maximum(0,6912),Minimum(4,0)