Finding tangent line

Question

Find an equation of the line tangent to the graph of y= 3/x^2 at the point (4/3/16)

Answer 1

At the point (4, 3/16) the slope of the tangent line to the graph of y = 3/x² can be found by evaluating y' at x = 4.

y = 3x^-2

y' = -6x^-3 = -6/x³

y'(4) = -6/64 = -3/32

Using point-slope:

y - 3/16 = (-3/32) ( x - 4)

y = (-3/32)x +3/8 + 3/16

y = (-3/32)x + 9/16 is the equation of the tangent line in slope-intercept form.

Visit this graph to see the tangent line at the given point. Use the moveable point to see other tangent lines to the curve.

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