What is the extreme 2x^5+5x^4,-2<= x<= 1 ?

The extreme 2x^5+5x^4,-2<= x<= 1 is Maximum(-2,16),Minimum(0,0),Maximum(1,7)

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extreme 2x^5+5x^4,-2<= x<= 1

extreme points

2 x^{5} + 5 x^{4}, - 2 \leq x \leq 1

Maximum (- 2, 16), Minimum (0, 0), Maximum (1, 7)

Solution steps

Find the critical points:

x = - 2, x = 0, x = 1

Domain of

2 x^{5} + 5 x^{4}, - 2 \leq x \leq 1 : - 2 \leq x \leq 1

Find intervals:

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < 1

Plug the extreme point

x = - 2

into

2 x^{5} + 5 x^{4} \Rightarrow y = 16

Maximum (- 2, 16)

Plug the extreme point

x = 0

into

2 x^{5} + 5 x^{4} \Rightarrow y = 0

Minimum (0, 0)

Plug the extreme point

x = 1

into

2 x^{5} + 5 x^{4} \Rightarrow y = 7

Maximum (1, 7)

Maximum (- 2, 16), Minimum (0, 0), Maximum (1, 7)

g (x) = \frac{2}{3} x^{3} - 2 x^{2}

f (x) = 6 x^{3} - 9 x^{2} - 216 x + 7

\frac{x}{x ^{2} + 64}

- (\frac{( 2 )}{( x ^{(2)} - 9 )})

f (x, y) = 121 - x^{2} - y^{2}

What is the extreme 2x^5+5x^4,-2<= x<= 1 ?
The extreme 2x^5+5x^4,-2<= x<= 1 is Maximum(-2,16),Minimum(0,0),Maximum(1,7)