Question
Using the properties of $f(x)=e^{x}$, show that $e^{x} \geq 1+x$ for all $x$.
Step 1
We want to show that $g(x) \geq 0$ for all $x$. Show more…
Show all steps
Your feedback will help us improve your experience
James Kiss and 69 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find $f^{-1}$ and verify that $\left(f \circ f^{-1}\right)(x)=\left(f^{-1} \circ f\right)(x)=x$. $$ f(x)=x^{2}+2 x+1, \quad x \geq-1 $$
Prerequisites for Calculus
Inverse Functions and Logarithms
Find $f^{-1}$ and verify that $\left(f \circ f^{-1}\right)(x)=\left(f^{-1} \circ f\right)(x)=x$. $$ f(x)=x^{2}+1, \quad x \geq 0 $$
$$ \begin{aligned} &\text { Given }\\ &\begin{aligned} f(x) &=e^{x}, \quad x \geq 0 \\ &=x+1, \quad x<0 \end{aligned} \end{aligned} $$ $$ \text { Find } f^{\prime}(0) \text { . } $$
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD