b) Is the following function continuous at x-1 and why? + 2x+1 (f*≥1 f(x)= 3x + 1 if x < 1 Q4: a) By using the definition of the derivative, find of y-sinx b) Find if y- sin (Set), 1-sec¹ (tanh w), w- 3rosh

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?

Determine whether each of the following statements is true or false, and explain why. The derivative of a quotient is the quotient of the derivatives.

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