What is the extreme 110t^2e^{-1.2t} ?

The extreme 110t^2e^{-1.2t} is Minimum(0,0),Maximum(5/3 ,41.35244…)

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extreme 110t^2e^{-1.2t}

extreme points

110 t^{2} e^{- 1.2 t}

Minimum (0, 0), Maximum (\frac{5}{3}, 41.35244 \dots)

Solution steps

Find the critical points:

t = 0, t = \frac{5}{3}

Domain of

110 t^{2} e^{- 1.2 t} : - \infty < t < \infty

Find intervals:

Decreasing

: - \infty < t < 0,

Increasing

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

Decreasing

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

Plug the extreme point

x = 0

into

110 t^{2} e^{- 1.2 t} \Rightarrow y = 0

Minimum (0, 0)

Plug the extreme point

x = \frac{5}{3}

into

110 t^{2} e^{- 1.2 t} \Rightarrow y = 41.35244 \dots

Maximum (\frac{5}{3}, 41.35244 \dots)

Minimum (0, 0), Maximum (\frac{5}{3}, 41.35244 \dots)

f (x) = - x^{3} + 6 x^{2} + x - 1

\frac{3 x ^{2}}{x ^{2} - 4}

y = \frac{x ^{3}}{x ^{2} - 4}

f (x) = 1 - e^{- k x}

f (x, y) = x^{2} - y^{2} - 2 x + 4 y + 6

What is the extreme 110t^2e^{-1.2t} ?
The extreme 110t^2e^{-1.2t} is Minimum(0,0),Maximum(5/3 ,41.35244…)