What is the extreme f(x)=0.01x^3-0.45x^2+2.43x+300 ?

The extreme f(x)=0.01x^3-0.45x^2+2.43x+300 is Maximum(3,303.51),Minimum(27,234.39)

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extreme f(x)=0.01x^3-0.45x^2+2.43x+300

extreme points

f (x) = 0.01 x^{3} - 0.45 x^{2} + 2.43 x + 300

Maximum (3, 303.51), Minimum (27, 234.39)

Solution steps

f^{'} (x) = 0.03 x^{2} - 0.9 x + 2.43

Find intervals:

Increasing

: - \infty < x < - 144 + 15,

Decreasing

: - 144 + 15 < x < 144 + 15,

Increasing

: 144 + 15 < x < \infty

Plug

x = 3

into

0.01 x^{3} - 0.45 x^{2} + 2.43 x + 300 : 303.51

Maximum (3, 303.51)

Plug

x = 27

into

0.01 x^{3} - 0.45 x^{2} + 2.43 x + 300 : 234.39

Minimum (27, 234.39)

Maximum (3, 303.51), Minimum (27, 234.39)

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

f (x) = \frac{1}{2} x^{4} - 4 x^{3} + 8 x^{2} + 46

f (x) = - x^{4} + 8 x^{2} + 5

f (x) = 3 x^{2} - 12 x

f (x) = 2 x^{4} + 16 x^{3} + 27

What is the extreme f(x)=0.01x^3-0.45x^2+2.43x+300 ?
The extreme f(x)=0.01x^3-0.45x^2+2.43x+300 is Maximum(3,303.51),Minimum(27,234.39)