What is the extreme f(x)=x^4+18x^2+5,-6<= x<= 6 ?

The extreme f(x)=x^4+18x^2+5,-6<= x<= 6 is Maximum(-6,1949),Minimum(0,5),Maximum(6,1949)

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extreme f(x)=x^4+18x^2+5,-6<= x<= 6

extreme points

f (x) = x^{4} + 18 x^{2} + 5, - 6 \leq x \leq 6

Maximum (- 6, 1949), Minimum (0, 5), Maximum (6, 1949)

Solution steps

Find the critical points:

x = - 6, x = 0, x = 6

Domain of

x^{4} + 18 x^{2} + 5, - 6 \leq x \leq 6 : - 6 \leq x \leq 6

Find intervals:

Decreasing

: - 6 < x < 0,

Increasing

: 0 < x < 6

Plug the extreme point

x = - 6

into

x^{4} + 18 x^{2} + 5 \Rightarrow y = 1949

Maximum (- 6, 1949)

Plug the extreme point

x = 0

into

x^{4} + 18 x^{2} + 5 \Rightarrow y = 5

Minimum (0, 5)

Plug the extreme point

x = 6

into

x^{4} + 18 x^{2} + 5 \Rightarrow y = 1949

Maximum (6, 1949)

Maximum (- 6, 1949), Minimum (0, 5), Maximum (6, 1949)

\frac{( x - 1 )}{( x ^{2} - x + 1 )}

f (x) = (x^{2} - 4 y^{2}) e^{1 - x^{2} - y^{2}}

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

f (x) = (x - 10)^{\frac{1}{3}}

y = (2 x - 1)^{2}

What is the extreme f(x)=x^4+18x^2+5,-6<= x<= 6 ?
The extreme f(x)=x^4+18x^2+5,-6<= x<= 6 is Maximum(-6,1949),Minimum(0,5),Maximum(6,1949)