# Thread: another trig tangent line equation

1. ## another trig tangent line equation

So I have to find the equation of the tangent line then use the second derivative to see if the graph lies above or below the tangent line

the function is

$f(x) = x \sin 2x$ with a given x value of $x = \pi/4$ and so $f'(x) = \sin 2x + 2x \cos 2x$ and $f"(x) = 4(\cos 2x - x \sin 2x)$

when I solve $f(\frac{\pi}{4}) = \frac{\pi}{4}$

so this would just mean $y=x$ or I could say $\frac{\pi}{4} - y = \frac{\pi}{4} - x$

correct?

And the graph lies below the tangent line because solving because $f"(x) < 0$ as shown $f"(\frac{\pi}{4}) = - \pi$