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How do you find the slope of the tangent line to the graph of the given function # f(x)= 2x-x^2#; x=0?

Answer 1

Isaiah Allen

#2#

The slope of a tgangent line to a curve in a Point #(x_0,y_0)# is given by

#f'(x_0)#

differentiating #f(x)# with respect to #x# we get

#f'(x)=2-2x#

so #f'(0)=2#

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Answer 2

Emilia Aguilar

#"slope "=2#

#"the slope of the tangent line "=f'(0)#

#f'(x)=2-2x#

#f'(0)=2-0=2larrcolor(blue)"slope of tangent line"#

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Answer 3

Isabella Ackerman

To find the slope of the tangent line to the graph of the function f(x) = 2x - x^2 at x = 0, we can use the derivative of the function. The derivative of f(x) is given by f'(x) = 2 - 2x.

To find the slope at x = 0, we substitute x = 0 into the derivative: f'(0) = 2 - 2(0) = 2.

Therefore, the slope of the tangent line to the graph of f(x) = 2x - x^2 at x = 0 is 2.

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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.