How do you find the equation of the line tangent to #y=-x^2# at (0,0)?

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Answer 1 · 2016-12-08T20:37:53

Please see the explanation.

Find the slope of the tangent line by computing the first derivative and then evaluate it at the desired x coordinate.

Compute the first derivative:

#dy/dx = -2x#

The desired x coordinate is 0, therefore the slope, m, is:

#m = -2(0)#

#m = 0#

Use the point-slope form of the equation of a line:

#y = m(x - x_1) + y_1#

Substitute 0 for #m, x_1, and y_1#:

#y = 0(x - 0) + 0#

The equation of the tangent line is:

#y = 0#