What is the extreme f(x)=2x^2-6x+4,0<= x<= 10 ?

The extreme f(x)=2x^2-6x+4,0<= x<= 10 is Maximum(0,4),Minimum(3/2 ,-1/2),Maximum(10,144)

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extreme f(x)=2x^2-6x+4,0<= x<= 10

extreme

Maximum (0, 4), Minimum (\frac{3}{2}, - \frac{1}{2}), Maximum (10, 144)

Solution steps

Find the critical points:

x = 0, x = \frac{3}{2}, x = 10

Domain of

2 x^{2} - 6 x + 4, 0 \leq x \leq 10 : 0 \leq x \leq 10

Find intervals:

Decreasing

: 0 < x < \frac{3}{2},

Increasing

: \frac{3}{2} < x < 10

Plug the extreme point

x = 0

into

2 x^{2} - 6 x + 4 \Rightarrow y = 4

Maximum (0, 4)

Plug the extreme point

x = \frac{3}{2}

into

2 x^{2} - 6 x + 4 \Rightarrow y = - \frac{1}{2}

Minimum (\frac{3}{2}, - \frac{1}{2})

Plug the extreme point

x = 10

into

2 x^{2} - 6 x + 4 \Rightarrow y = 144

Maximum (10, 144)

Maximum (0, 4), Minimum (\frac{3}{2}, - \frac{1}{2}), Maximum (10, 144)

What is the extreme f(x)=2x^2-6x+4,0<= x<= 10 ?
The extreme f(x)=2x^2-6x+4,0<= x<= 10 is Maximum(0,4),Minimum(3/2 ,-1/2),Maximum(10,144)