I know how to make the graph of this but I don't know how to find the points. when I graph it and check the intercepts I get decimals but don't know how to make it in radians. ### Problem Statement**Objective:**Determine all points on the curve \( y = 4 \tan x \) within the interval \(-\frac{\pi}{2} < x < \frac{\pi}{2}\), such that the tangent line at these points is parallel to the line \( y = 8x \).**Detailed Explanation:**To find the solution, follow these steps:1. **Function and Interval:** - Curve: \( y = 4 \tan x \) - Interval: \( -\frac{\pi}{2} < x < \frac{\pi}{2} \)2. **Tangent Line Parallel Condition:** - The slope of the tangent line to the curve \( y = 4 \tan x \) should be equal to the slope of the line \( y = 8x \). - The slope of \( y = 8x \) is given as 8.3. **Finding the Derivative:** - Derivative of \( y = 4 \tan x \) is \( y' = 4 \sec^2 x \).4. **Setting the Derivative Equal to the Slope:** - \( 4 \sec^2 x = 8 \)5. **Solving for \( x \):** - \( \sec^2 x = 2 \) - \( \cos^2 x = \frac{1}{2} \) - \( \cos x = \pm \frac{1}{\sqrt{2}} \) - \( x = \pm \frac{\pi}{4} \)6. **Finding Corresponding \( y \)-values:** - For \( x = \frac{\pi}{4} \): \( y = 4 \tan \left( \frac{\pi}{4} \right) = 4 \cdot 1 = 4 \). - For \( x = -\frac{\pi}{4} \): \( y = 4 \tan \left( -\frac{\pi}{4} \right) = 4 \cdot (-1) = -4 \).7. **Solution Points:** - \( \left( \frac{\pi}{4}, 4 \right) \) - \( \left( -\frac{\pi}{4}, -4 \right)

Name: I know how to make the graph of this but I don't know how to find the
Uploaded: 2024-03-20T07:06:16.000Z
Channel: Bartleby
Description: I know how to make the graph of this but I don't know how to find the points. when I graph it and check the intercepts I get decimals but don't know how to make it in radians. ### Problem Statement**Objective:**Determine all points on the curve \( y