How do you find the slope of a tangent line to the graph of the function #y = x^2 + x - 2# at x=-2?

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Answer 1 · 2016-11-29T00:29:12

# y = -3x-6 #

#y = x^2+x-2#

The slope of the tangent at any particular point is given by the derivative at that point.

Differentiating wrt #x# we get;

# dy/dx = 2x+1 #

When #x=-2 => dy/dx = -4+1 = -3#
And, #x=-2 => y = 4-2-2 = 0#

So the tangent passes through #(-2,0)# and has slope #-3#

Using, #y - y_1=m(x=x_1)# the required equation is:

# y - 0 = -3(x-(-2)) #
# :. y = -3x-6 #

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