Interval y = 2(csc x + sec x) 0 < x < 𝜋/2

Question

Analyze and sketch a graph of the function over the given interval. Label any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.)

Function: y = 2(csc x + sec x)

Interval: 0 < x < 𝜋/2

Find the relative minimum

Find the equations of the asymptotes. (Enter your answers as a comma-separated list of equations. Include asymptotes that fall within the closed interval 0 ≤ x ≤ 𝜋/2.

 (If an answer does not exist, enter DNE.)

Answer 1

go to desmos or another online graphing calculator

punch in 2(csc(x) + sec(x)) and it gives you in 1 second the graph, showing only one x intercept in the range of 0 to pi/2

about 2+ something.

cscx + secx = 0

it's usually easier to visualize what goes on if you convert to sines and cosines

1/sinx + 1/cosx = 0

multiply by sinxcosx to get

cosx +sinx = 0

that requires either sinx or cosx to be negative which isn't possible in quadrant I or when 0<x<pi/2

so there is no solution for x intercepts. As to that part DNE