What is the equation of the tangent line of #f(x)=x^2 + 2x # at #x=3#?

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Answer 1 · 2016-01-18T13:48:32

The tangent line is # y = 8x - 9#

Differentiate the equation to find the gradient.
#f'(x) = 2x +2#

At the point #x = 3# this equals #8# which is the gradient.

The equation for the tangent is # y = mx + c# where #m# is the gradient and #c# is the y-intercept.

We can find #c# by using the coordinates of the specified point.

At #x=3# , #y = 3^2 +2*3 =15#

This point is also on the tangent line, so we can say #15 = 8*3 + c#
Therefore # c = 15 - 24 = -9#

The tangent line is # y = 8x - 9#