Horizontal Tangent Line

Question

At what value of x does the function sin^-1(2x) . cos^-1(2x) have the horizontal tangent line

Answer 1

the assumption is

f(x)=[cos^-1(2x)]*sin^-1(2x)

f'(x)=[sin^-1(2x)]*-2(1-4x²)^-(1/2)+[cos^-1(2x)]*2(1-4x²)^-(1/2)

f'(x)=0

when sin^-1(2x)=cos^-1(2x)

2x=sin(cos^-1(2x))=+/-(1-4x²)^1/2

4x²=(1-4x²)

x=+/-√(1/8),,,,the negative answer does not have sin^-1(2x)=cos^-1(2x)

x= √(1/8)

Answer 2

Hi! For this problem you would have to differentiate the function and set it equal to zero. This is because a horizontal tangent line just means when is the slope equal to the zero. I'm not sure what the exact function is, but you can figure out the derivative using a calculator or re-examining the arc-trig derivative rules.