your derivative is correct.
now just plug in x = π/2 to get the slope
remember that tan(π/2) is undefined, BUT
cot (π/2) = cos(π/2) / sin(π/2) = 0/1 = 0
so slope = -csc^2 (π/2) = 2
equation of tangent:
y-1 = 2(x- π/2)
clean it up if needed.
for a horizontal tangent, remember that a horizontal line has a slope of 0.
Find an equation for the tangent line to the curve at (π/2 , 2).
y = 4 + cot(x) - 2csc(x)
I am confused how to take the derivative of this problem. When I tried to solve it I ended up with
-csc^2 (x) + (2csc(x) * cot(x)).
From there I can't seem to simplify it.
Also, can you explain how to find the horizontal tangent.
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I calculated and got -1 as the slope. Can you please explain how you got 2 for the slope?
1 answer