Question 1\ 1 pts\ Consider function

f(x)

. Let

y=L(x)

be the line that is tangent to the graph of

y=f(x)

at the point where

x=a

.\ Which of the following statements are true? Select all that apply.\ They both pass through the same point at

a

, so

f(a)=L(a)

.\ They both have the same concavity at

a

, so

*f^('')(a)=L^('')(a)

.\ They look the same when you zoom in close enough.\ They both have the same derivative at

a

, so

f^(')(a)=L^(')(a)

.\ Question 2\ 1 pts\ What property or properties does the function

f(x)=e^(x)

share with its quadratic approximation at

x=0

,

P_(2)(x)

, shown in this video? Select all that apply.\ They both pass through the same point at

a

, so

f(0)=P_(2)(0)

.\ They both have the same concavity at

x=0

, so

f^('')(0)=P_(2)^('')(0)

.\ They look the same when you zoom in close enough.\ They both have the same derivative at

a

, so

f^(')(a)=P_(2)^(')(a)

.

Consider function f(x). Let y=L(x) be the line that is tangent to the graph of y=f(x) at the point where x=a. Which of the following statements are true? Select all that apply. They both pass through the same point at a, so f(a)=L(a). They both have the same concavity at a, so f(a)=L(a). They look the same when you zoom in close enough. They both have the same derivative at a, so f(a)=L(a). Question 2 1pts What property or properties does the function f(x)=ex share with its quadratic approximation at x=0, P2(x), shown in this video? Select all that apply. They both pass through the same point at a, so f(0)=P2(0). They both have the same concavity at x=0, so f(0)=P2(0). They look the same when you zoom in close enough. They both have the same derivative at a, so f(a)=P2(a)