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Popular Functions >

extreme f(x)=3t^4+4t^3-6t^2

Solution

extreme points

f (x) = 3 t^{4} + 4 t^{3} - 6 t^{2}

Solution

Minimum (\frac{- 1 - 5}{2}, \frac{3 ( - 1 - 5 ) ^{4}}{16} - 17 - 75), Maximum (0, 0), Minimum (\frac{- 1 + 5}{2}, \frac{3 ( 5 - 1 ) ^{4}}{16} + 75 - 17)

Solution steps

f^{'} (t) = 12 t^{3} + 12 t^{2} - 12 t

Find intervals:

Decreasing

: - \infty < t < \frac{- 1 - 5}{2},

Increasing

: \frac{- 1 - 5}{2} < t < 0,

Decreasing

: 0 < t < \frac{5 - 1}{2},

Increasing

: \frac{5 - 1}{2} < t < \infty

Plug

t = \frac{- 1 - 5}{2}

into

3 t^{4} + 4 t^{3} - 6 t^{2} : \frac{3 ( - 1 - 5 ) ^{4}}{16} - 17 - 75

Minimum (\frac{- 1 - 5}{2}, \frac{3 ( - 1 - 5 ) ^{4}}{16} - 17 - 75)

Plug

t = 0

into

3 t^{4} + 4 t^{3} - 6 t^{2} : 0

Maximum (0, 0)

Plug

t = \frac{- 1 + 5}{2}

into

3 t^{4} + 4 t^{3} - 6 t^{2} : \frac{3 ( 5 - 1 ) ^{4}}{16} + 75 - 17

Minimum (\frac{- 1 + 5}{2}, \frac{3 ( 5 - 1 ) ^{4}}{16} + 75 - 17)

Minimum (\frac{- 1 - 5}{2}, \frac{3 ( - 1 - 5 ) ^{4}}{16} - 17 - 75), Maximum (0, 0), Minimum (\frac{- 1 + 5}{2}, \frac{3 ( 5 - 1 ) ^{4}}{16} + 75 - 17)

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=3t^4+4t^3-6t^2 ?
The extreme f(x)=3t^4+4t^3-6t^2 is