Calculus of Exponential Functions

Consider the function $f\left(x\right)=3-e^{-x}$`f`(`x`)=3−`e`−`x`.

a

Determine $f\left(0\right)$`f`(0).

b

Determine $f'\left(0\right)$`f`′(0).

c

Which of the following statements is true?

$f'\left(x\right)<0$`f`′(`x`)<0 for $x\ge0$`x`≥0

A

$f'\left(x\right)<0$`f`′(`x`)<0 for all real $x$`x`.

B

$f'\left(x\right)>0$`f`′(`x`)>0 for all real $x$`x`.

C

$f\left(x\right)>0$`f`(`x`)>0 for all real $x$`x`.

D

$f'\left(x\right)<0$`f`′(`x`)<0 for $x\ge0$`x`≥0

A

$f'\left(x\right)<0$`f`′(`x`)<0 for all real $x$`x`.

B

$f'\left(x\right)>0$`f`′(`x`)>0 for all real $x$`x`.

C

$f\left(x\right)>0$`f`(`x`)>0 for all real $x$`x`.

D

d

Determine the value of $\lim_{x\to\infty}f\left(x\right)$lim`x`→∞`f`(`x`).

Easy

Approx 4 minutes

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