Find the tangent line to the graph of f(x) = $\cos ^ { 2 }$ 2x at $\frac { \pi } { 2 } , 1$ .
A) 2
B) -2
C) -1
D) 1
E) none of these

Question

Quizplus · Accepted Answer

To find the tangent line to the graph of $f(x) = \cos^2(2x)$ at the point $\frac{\pi}{2}, 1$, we first need to find the derivative of $f(x)$, which gives us the slope of the tangent line at any point $x$. The derivative of $f(x)$ with respect to $x$ is found using the chain rule:$$f'(x) = 2\cos(2x)(-2\sin(2x)) = -4\sin(2x)\cos(2x) = -4\sin(4x)/2 = -2\sin(4x).$$To find the slope of the tangent line at $x = \frac{\pi}{2}$, we substitute $x = \frac{\pi}{2}$ into the derivative:$$f'\left(\frac{\pi}{2}\right) = -2\sin(4 \cdot \frac{\pi}{2}) = -2\sin(2\pi) = -2 \cdot 0 = 0.$$The slope of the tangent line at $\frac{\pi}{2}$ is 0, which is not among the given choices, so the correct answer is E) none of these.

Find the Tangent Line to the Graph of F(x) = cos⁡2\cos ^ { 2 }cos2

Find the Tangent Line to the Graph of F(x) = $\cos ^ { 2 }$