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How do you find the slope of the tangent line to the graph of the given function # y=x^2#; at (2,3)?

Answer 1

Luke Alvarez

here, let f(x) =y = #x^2#

f'(x) will give you the slope of tangent

So , f'(x) = #dx^2/dy # =2x So 2x is the slope of the tangent.

TO find the slope of tangent at the point where x=2,

we have,

Slope(m) = 2*2 = 4

So the equation of tangent with slope 4 and passing through (2,3) is given by; (y-y1)=m(x-x1) (y-3) =4(x-2) y-3 = 4x - 8 So, y= 4x-5 is the equation of the tangent of the curve y= #x^2# at the point (2,3)

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Answer 2

Isaiah Allen

To find the slope of the tangent line to the graph of the function y=x^2 at the point (2,3), we can use the derivative of the function. The derivative of y=x^2 is given by dy/dx = 2x.

To find the slope at a specific point, substitute the x-coordinate of the point into the derivative. In this case, substitute x=2 into dy/dx = 2x.

Therefore, the slope of the tangent line to the graph of y=x^2 at (2,3) is 2(2) = 4.

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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.