Consider the following function. f(x) sin χ ,x % 0 ,x=0 Prove that f is discontinuous at x=0 Prove that f is continuous for x = 0

Use graphical differentiation to verify that ddxex=ex.

Where is the function defined by f(x)=ex increasing? Decreasing? Where is the tangent line horizontal?

Margy and Nate are working on taking the derivative of fx=23x+14. Margy uses the quotient rule and chain rule as follows: f'x=3x+140-243x+1333x+18 f'x=-243x+133x+18=-243x+15. Nate rewrites the function and uses the power rule and chain rule as follows: fx=23x+1-4 f'x=-423x+1-53=-243x+15. Compare the two procedures. Which procedure do you think is preferable?