What is the extreme f(x)=6+81x-3x^3,0<= x<= 4 ?

The extreme f(x)=6+81x-3x^3,0<= x<= 4 is Minimum(0,6),Maximum(3,168),Minimum(4,138)

Popular >

extreme f(x)=6+81x-3x^3,0<= x<= 4

extreme points

f (x) = 6 + 81 x - 3 x^{3}, 0 \leq x \leq 4

Minimum (0, 6), Maximum (3, 168), Minimum (4, 138)

Solution steps

Find the critical points:

x = 0, x = 3, x = 4

Domain of

6 + 81 x - 3 x^{3}, 0 \leq x \leq 4 : 0 \leq x \leq 4

Find intervals:

Increasing

: 0 < x < 3,

Decreasing

: 3 < x < 4

Plug the extreme point

x = 0

into

6 + 81 x - 3 x^{3} \Rightarrow y = 6

Minimum (0, 6)

Plug the extreme point

x = 3

into

6 + 81 x - 3 x^{3} \Rightarrow y = 168

Maximum (3, 168)

Plug the extreme point

x = 4

into

6 + 81 x - 3 x^{3} \Rightarrow y = 138

Minimum (4, 138)

Minimum (0, 6), Maximum (3, 168), Minimum (4, 138)

f (x) = \frac{x ^{2} + 69}{x + 10}

\frac{t ^{2}}{t + 3}

f (x) = x^{3} - 10 x + 25 x - 2

f (x) = \frac{20}{x} + 2 π x^{2}, x > 0

f (x) = - x^{3} + x^{2} + 11 x - 1

What is the extreme f(x)=6+81x-3x^3,0<= x<= 4 ?
The extreme f(x)=6+81x-3x^3,0<= x<= 4 is Minimum(0,6),Maximum(3,168),Minimum(4,138)