What is the extreme 6x^5+33x^4-30x^3+100 ?

The extreme 6x^5+33x^4-30x^3+100 is Maximum(-5,5725),Saddle(0,100),Minimum(3/5 , 307073/3125)

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extreme 6x^5+33x^4-30x^3+100

extreme

Maximum (- 5, 5725), Saddle (0, 100), Minimum (\frac{3}{5}, \frac{307073}{3125})

Solution steps

f^{'} (x) = 30 x^{4} + 132 x^{3} - 90 x^{2}

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < 0,

Decreasing

: 0 < x < \frac{3}{5},

Increasing

: \frac{3}{5} < x < \infty

Plug

x = - 5

into

6 x^{5} + 33 x^{4} - 30 x^{3} + 100 : 5725

Maximum (- 5, 5725)

Plug

x = 0

into

6 x^{5} + 33 x^{4} - 30 x^{3} + 100 : 100

Saddle (0, 100)

Plug

x = \frac{3}{5}

into

6 x^{5} + 33 x^{4} - 30 x^{3} + 100 : \frac{307073}{3125}

Minimum (\frac{3}{5}, \frac{307073}{3125})

Maximum (- 5, 5725), Saddle (0, 100), Minimum (\frac{3}{5}, \frac{307073}{3125})

What is the extreme 6x^5+33x^4-30x^3+100 ?
The extreme 6x^5+33x^4-30x^3+100 is Maximum(-5,5725),Saddle(0,100),Minimum(3/5 , 307073/3125)