Question

find the slope of the tangent to the fnction 4tan^(2)x at the point x=pi/4

Answer 1

i am getting 16 as the slope am i wrong ??

Answer 2

i toke the dervative and i got 8tan(pi/4)secx(pi/4)^(2)

Answer 3

looks good, yes

Answer 4

\(\bf sec^2\left(\frac{\pi}{4}\right)\implies sec^2\left(\frac{2}{\sqrt{2}}\right)\implies \cfrac{4}{2}\implies 2\)

and the \(\bf tan\left(\frac{\pi}{4}\right)=1\)

Answer 5

so i am right??

Answer 6

yeap

Answer 7

wow

Answer 8

i did it so quickly i felt it was wrong

Answer 9

\(\bf sec^2\left({\color{blue}{ \frac{\pi}{4}}}\right)\implies sec^2\left(\frac{2}{\sqrt{2}}\right)\implies \cfrac{4}{2}\implies 2
\\ \quad \\

tan\left({\color{blue}{ \frac{\pi}{4}}}\right)\implies 1
\\ \quad \\ \quad \\
------------------------\\
\cfrac{c}{dx}[4tan^2(x)]\implies 4\cdot 2tan(x)\cdot sec^2(x)
\\ \quad \\

4\cdot 2tan\left({\color{blue}{ \frac{\pi}{4}}}\right)\cdot sec^2\left({\color{blue}{ \frac{\pi}{4}}}\right)\implies 4\cdot 2\cdot 1\cdot 2\)

Answer 10

hmm ahemm \(\bf sec^2\left({\color{blue}{ \frac{\pi}{4}}}\right)\implies sec^2\left(\frac{2}{\sqrt{2}}\right)\implies \cfrac{4}{2}\implies 2
\\ \quad \\

tan\left({\color{blue}{ \frac{\pi}{4}}}\right)\implies 1
\\ \quad \\ \quad \\
------------------------\\
\cfrac{d}{dx}[4tan^2(x)]\implies 4\cdot 2tan(x)\cdot sec^2(x)
\\ \quad \\

4\cdot 2tan\left({\color{blue}{ \frac{\pi}{4}}}\right)\cdot sec^2\left({\color{blue}{ \frac{\pi}{4}}}\right)\implies 4\cdot 2\cdot 1\cdot 2\)

Answer 11

my method is also correct right ? ?

Answer 12

well, I assume you used that =)
but it's 16, yes