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How do you find all points on the graph of #f(x)=sin^2x# at which the tangent line is horizontal?

Answer 1

Christopher Agresta

graph{(sinx)^2 [-10, 10, -5, 5]}

#kpi/2 \ \ \ ;\ \ \ kinZZ#

#f^'(x)=2sinxcosx=sin2x#

#sin(2x)=0\ \ \ # when #\ \ \ \2x=kpi\ \ \ ; \ \ \ k in ZZ#

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Answer 2

Luke Alvarez

To find all points on the graph of ( f(x) = \sin^2 x ) at which the tangent line is horizontal, you need to determine where the derivative of the function equals zero. First, find the derivative of ( f(x) ) with respect to ( x ), denoted as ( f'(x) ). Then, set ( f'(x) ) equal to zero and solve for ( x ). These values of ( x ) will correspond to the points on the graph where the tangent line is horizontal.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.