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Slope of a curve #y=x^2-3# at the point where #x=1#?

Answer 1

Emma Aldridge

First you need to find #f'(x)#, which is the derivative of #f(x)#.

#f'(x)=2x-0=2x#

Second, substitute in the value of x, in this case #x=1#.

#f'(1)=2(1)=2#

The slope of the curve #y=x^2-3# at the #x# value of #1# is #2#.

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Answer 2

Paisley Johnson

To find the slope of the curve ( y = x^2 - 3 ) at the point where ( x = 1 ), you need to find the derivative of the function and then evaluate it at ( x = 1 ). The derivative of ( y = x^2 - 3 ) is ( \frac{dy}{dx} = 2x ).

Substitute ( x = 1 ) into the derivative:

( \frac{dy}{dx} = 2(1) = 2 )

So, the slope of the curve ( y = x^2 - 3 ) at the point where ( x = 1 ) 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.