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# Find the Coordinate of the point on the graph of y=f(x) in [-1,1] where the gradient of the tangent line to the curve is 0

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I got part A, as $$x = {}\frac{1-2x}{\sqrt{1-x^2}}$$

Just need help with part B

Mar 12, 2021
edited by SpaceTsunaml  Mar 12, 2021

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So your question is looking for where the tangent line has zero slope in the interval between  -1 and 1  inclusive

If you properly derived the derivative,  set it equal  to 0   and find where in the inteval requested, it = zero

The derivative of a funtion IS the slope of the function     ....... given f(x)     f ' (x) is the slope.....(  gradient is the same thing as slope.)

1-2x / (sqrt1-x^2)    = 0

1-2x = 0

-2x = -1

x = 1/2

Mar 12, 2021
edited by ElectricPavlov  Mar 12, 2021
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See I thought so, but my brain was thinking the gradient OF the derivative, but I felt that was wrong, but anyways yeah thats what I thought haha, it just seemed too simple! Lol my brain overthinking everything. Thank you :)

SpaceTsunaml  Mar 12, 2021