AP calculus exam tikx graph of e (tan x ) -2

[karush]

The graph of $y=e^{\tan x} - 2$ crosses the x-axis at one point in the interval [0,1]. What is the slope of the graph at this point.

A. 0.606
B 2
C 2.242
D 2.961
E 3.747ok i tried to do a simple graph of y= with tikx but after an hour trying failed
doing this in demos it seens the answer is D

I know you take the differential set it to zero and that should give you the x value of intersection

 

[skeeter]

The graph of $y=e^{\tan x} - 2$ crosses the x-axis at one point in the interval [0,1]. What is the slope of the graph at this point.

A. 0.606
B 2
C 2.242
D 2.961
E 3.747ok i tried to do a simple graph of y= with tikx but after an hour trying failed
doing this in demos it seens the answer is D

I know you take the differential set it to zero and that should give you the x value of intersection ?

AP exams are designed to utilize a hand-held calculator ...

Graph the function within the given interval, calculate the zero and store it a register, then calculate the derivative value at that zero.

 

[karush]

looks like a TI how did you get the screen shots?

 

[skeeter]

My ti84 emulator has a "take screenshot" capability

 

[Greg]

Observing that $y=e^{\tan x} - 2$ has a root in [0, 1] at $\text{atan}(\log2)$, we need to evaluate $2\sec^2(\text{atan}(\log2))$. That is approximately 2.961, hence choice D is correct.