What is the extreme f(x)=g(t)=6t^4-8t^3+5 ?

The extreme f(x)=g(t)=6t^4-8t^3+5 is Saddle(0,5),Minimum(1,3)

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extreme f(x)=g(t)=6t^4-8t^3+5

extreme points

f (x) = g (t) = 6 t^{4} - 8 t^{3} + 5

Saddle (0, 5), Minimum (1, 3)

Solution steps

f^{'} (t) = 24 t^{3} - 24 t^{2}

Find intervals:

Decreasing

: - \infty < t < 0,

Decreasing

: 0 < t < 1,

Increasing

: 1 < t < \infty

Plug

t = 0

into

6 t^{4} - 8 t^{3} + 5 : 5

Saddle (0, 5)

Plug

t = 1

into

6 t^{4} - 8 t^{3} + 5 : 3

Minimum (1, 3)

Saddle (0, 5), Minimum (1, 3)

f (x) = - \frac{x ^{2}}{8} + \frac{y ^{2}}{78.13} + 8

f (x) = - (x - 4)^{2} \cdot (x + 4)^{2}

f (x, y) = x^{2} + y^{2} - 2 x + 10 y - 15

f (x) = - x^{3} - x^{2} + 5 x - 4

f (x) = - x^{3} - x^{2} + 5 x - 5

What is the extreme f(x)=g(t)=6t^4-8t^3+5 ?
The extreme f(x)=g(t)=6t^4-8t^3+5 is Saddle(0,5),Minimum(1,3)