What is e^{(-t)/4}-(e^{-t/4}(t))/4 >= 0 ?

The solution to e^{(-t)/4}-(e^{-t/4}(t))/4 >= 0 is t<= 4

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e^{(-t)/4}-(e^{-t/4}(t))/4 >= 0

e^{\frac{- t}{4}} - \frac{e ^{- \frac{t}{4}} ( t )}{4} \geq 0

t \leq 4

Interval Notation

(- \infty, 4]

Solution steps

e^{\frac{- t}{4}} - \frac{e ^{- \frac{t}{4}} ( t )}{4} \geq 0

Apply exponent rules

e^{\frac{- t}{4}} - \frac{\frac{1}{e ^{\frac{t}{4}}} t}{4} \geq 0

f (x) > 0

we can multiply or devide both sides of inequality by

f (x)

e^{\frac{t}{4}}

is greater than

0

for all

t

e^{\frac{- t}{4}} e^{\frac{t}{4}} - \frac{\frac{1}{e ^{\frac{t}{4}}} t}{4} e^{\frac{t}{4}} \geq 0 \cdot e^{\frac{t}{4}}

Simplify

e^{- \frac{t}{4}} e^{\frac{t}{4}} - \frac{t}{4} \geq 0

Simplify

e^{- \frac{t}{4}} e^{\frac{t}{4}} - \frac{t}{4} : 1 - \frac{t}{4}

1 - \frac{t}{4} \geq 0

Move

1

to the right side

- \frac{t}{4} \geq - 1

Multiply both sides by

4

- t \geq - 4

Multiply both sides by

- 1

t \leq 4

\frac{x ^{2} - 81}{x ^{4} - 81} < 0

5 \cdot 50

9 x^{2} + 12 x - 5 = 0

- 5 x \leq 15

x^{2} + 7 x = 16

What is e^{(-t)/4}-(e^{-t/4}(t))/4 >= 0 ?
The solution to e^{(-t)/4}-(e^{-t/4}(t))/4 >= 0 is t<= 4