Home > Calculus > Slope of a Curve at a Point

For the curve #y=x-x^2#, how do you find the slope of the tangent line to the curve at (1,0)?

Answer 1

First you evaluate the derivative of your function #y'(x)#: Then you evaluate the derivative at #x=1#, or #y'(1)#, which is the slope of your tangent line. Try by yourself and if it doesn' work look below for the maths: . . . . . . . .

Solution: #y'(x)=1-2x# #y'(1)=1-2=-1#

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Answer 2

Adam Adkins

To find the slope of the tangent line to the curve ( y = x - x^2 ) at the point ( (1,0) ), you need to find the derivative of the function and then evaluate it at ( x = 1 ).

The derivative of the function ( y = x - x^2 ) is given by ( y' = 1 - 2x ).

Substituting ( x = 1 ) into the derivative, we get ( y'(1) = 1 - 2(1) = 1 - 2 = -1 ).

So, the slope of the tangent line to the curve at ( (1,0) ) is ( -1 ).

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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.