What is the extreme f(x)=1.3te^{-2.9t} ?

The extreme f(x)=1.3te^{-2.9t} is Maximum(10/29 ,0.16491…)

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extreme f(x)=1.3te^{-2.9t}

extreme points

f (x) = 1.3 t e^{- 2.9 t}

Maximum (\frac{10}{29}, 0.16491 \dots)

Solution steps

Find the critical points:

t = \frac{10}{29}

Domain of

1.3 t e^{- 2.9 t} : - \infty < t < \infty

Find intervals:

Increasing

: - \infty < t < \frac{10}{29},

Decreasing

: \frac{10}{29} < t < \infty

Plug the extreme point

x = \frac{10}{29}

into

1.3 t e^{- 2.9 t} \Rightarrow y = 0.16491 \dots

Maximum (\frac{10}{29}, 0.16491 \dots)

y = x \cdot 1 + x^{2}

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

f (x) = - 5 x + 2 ln (2 x)

\frac{x + 3}{x ^{2} - 2 x - 15}

f (x, y) = - (x + 1) 2 - (y + x) 2

What is the extreme f(x)=1.3te^{-2.9t} ?
The extreme f(x)=1.3te^{-2.9t} is Maximum(10/29 ,0.16491…)