What is the extreme f(x)=x^3-x^2-x+7 ?

The extreme f(x)=x^3-x^2-x+7 is Maximum(-1/3 , 194/27),Minimum(1,6)

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extreme f(x)=x^3-x^2-x+7

extreme points

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

Maximum (- \frac{1}{3}, \frac{194}{27}), Minimum (1, 6)

Solution steps

f^{'} (x) = 3 x^{2} - 2 x - 1

Find intervals:

Increasing

: - \infty < x < - \frac{1}{3},

Decreasing

: - \frac{1}{3} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - \frac{1}{3}

into

x^{3} - x^{2} - x + 7 : \frac{194}{27}

Maximum (- \frac{1}{3}, \frac{194}{27})

Plug

x = 1

into

x^{3} - x^{2} - x + 7 : 6

Minimum (1, 6)

Maximum (- \frac{1}{3}, \frac{194}{27}), Minimum (1, 6)

sin (x) - cos (x)

y = x + e^{- 4 x}

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

f (x) = 8 - x

f (x) = 2 sin (3 x) - 5

What is the extreme f(x)=x^3-x^2-x+7 ?
The extreme f(x)=x^3-x^2-x+7 is Maximum(-1/3 , 194/27),Minimum(1,6)