-apc.2.1.06 crosses the x-axis at one point in the interval [0,1]

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  • Thread starter karush
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  • #1
karush
Gold Member
MHB
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$\tiny{APC.2.1.06}$
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.3.747

[d]
$\begin{array}{rll}
\textit{given} &e^{\tan \:x}-2 &(1)\\
\textit{rewrite} &e^{\tan x}=2 &(2) \\
\textit{e thru} &\tan x=\ln 2 &(3)\\
\textit{isolate x } &x=\arctan \ln 2+\pi n &(4)\\
\textit{[0,1] } &\arctan(\ln 2)=0.606 &(5)\\
\textit{m at x} &y_m=e^{\tan (x)}\sec ^2(x) &(6)\\
\textit{m} &y_m(0.606)=2.96 &(7)
\end{array}$

it took me 2 hours to do this
must be a better way

if its correct:unsure:
 

Answers and Replies

  • #2
skeeter
1,104
1
fyi, this is a calculator active problem …

6695B933-7821-4557-9A00-DAC241A97F13.jpeg
 
  • #3
HOI
923
2
$\tiny{APC.2.1.06}$
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.3.747

[d]
$\begin{array}{rll}
\textit{given} &e^{\tan \:x}-2 &(1)\\
\textit{rewrite} &e^{\tan x}=2 &(2) \\
\textit{e thru} &\tan x=\ln 2 &(3)\\
\textit{isolate x } &x=\arctan \ln 2+\pi n &(4)\\
\textit{[0,1] } &\arctan(\ln 2)=0.606 &(5)\\
\textit{m at x} &y_m=e^{\tan (x)}\sec ^2(x) &(6)\\
\textit{m} &y_m(0.606)=2.96 &(7)
\end{array}$

it took me 2 hours to do this
must be a better way

if its correct:unsure:
You mean "given $e^{\tan(x)}-2= 0$". Otherwise your second line makes no sense!
 
  • #4
karush
Gold Member
MHB
3,267
4
ok guess I was assuming that
fyi, this is a calculator active problem …

View attachment 11165
what graphing program is that from?
doesnt look like Desmos
 
  • #5
skeeter
1,104
1
ok guess I was assuming that

what graphing program is that from?
doesnt look like Desmos

Good Grapher Pro app on my ipad.
 

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