How do you find the equation of the line tangent to the graph of #y = sqrtx# at (16,4)?

Answer 1

#y=1/8x+2#

#"to obtain the equation we require the slope m and a "# #"point on the tangent"#
#"the point "(x_1,y_1)=(16,4)#
#m_(color(red)"tangent")=dy/dx" at x = 16"#
#y=sqrtx=x^(1/2)#
#rArrdy/dx=1/2x^(-1/2)=1/(2x^(1/2))=1/(2sqrtx)#
#x=16tody/dx=1/(2xx4)=1/8#
#rArry-4=1/8(x-16)#
#rArry=1/8x+2larrcolor(red)"equation of tangent"#
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Answer 2

To find the equation of the line tangent to the graph of y = sqrt(x) at the point (16,4), we can use the derivative of the function.

First, we find the derivative of y = sqrt(x) with respect to x, which is 1/(2*sqrt(x)).

Next, we substitute x = 16 into the derivative to find the slope of the tangent line at that point.

The slope of the tangent line is 1/(2*sqrt(16)) = 1/8.

Using the point-slope form of a linear equation, we have y - 4 = (1/8)(x - 16).

Simplifying the equation, we get y = (1/8)x + 2.

Therefore, the equation of the line tangent to the graph of y = sqrt(x) at (16,4) is y = (1/8)x + 2.

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Answer 3

To find the equation of the line tangent to the graph of (y = \sqrt{x}) at the point (16,4), you need to find the slope of the tangent line at that point, then use point-slope form to write the equation of the tangent line.

  1. Find the derivative of the function (y = \sqrt{x}). [ \frac{dy}{dx} = \frac{1}{2\sqrt{x}} ]

  2. Evaluate the derivative at x = 16 to find the slope of the tangent line at that point. [ \frac{dy}{dx} \bigg|_{x=16} = \frac{1}{2\sqrt{16}} = \frac{1}{8} ]

  3. Use the point-slope form of a line with point (16,4) and slope (\frac{1}{8}). [ y - y_1 = m(x - x_1) ] [ y - 4 = \frac{1}{8}(x - 16) ]

  4. Simplify to get the equation in slope-intercept form, if necessary. [ y - 4 = \frac{1}{8}x - 2 ] [ y = \frac{1}{8}x + 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.

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.

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.

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.

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