What is the extreme f(x)=-x^3+3x+1 ?

The extreme f(x)=-x^3+3x+1 is Minimum(-1,-1),Maximum(1,3)

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extreme f(x)=-x^3+3x+1

extreme points

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

Minimum (- 1, - 1), Maximum (1, 3)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

- x^{3} + 3 x + 1 : - 1

Minimum (- 1, - 1)

Plug

x = 1

into

- x^{3} + 3 x + 1 : 3

Maximum (1, 3)

Minimum (- 1, - 1), Maximum (1, 3)

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

- x^{3} - 3 x^{2}

f (x) = 2 x - 4 sin (x), 0 \leq x \leq 2 π

f (x) = \frac{x ^{3}}{3} - 2 x^{2} + 4, - 2 \leq x \leq 1

f (x, y) = x^{4} + 6 y^{2} - 4 x y^{3} - 1

What is the extreme f(x)=-x^3+3x+1 ?
The extreme f(x)=-x^3+3x+1 is Minimum(-1,-1),Maximum(1,3)