How do you find the equation of the tangent to the curve #y=x^2+2x-5# that is parallel to the line #y=4x-1#?

1 Answer
Daniel L.
May 20, 2015

The tangent line is #y=4x+3#

To calculate this you have to follow these steps:

1) The tangent line is parallel to #y=4x+1#, so it has a form of #y=4x+c#. (1)
2) You have to find the point where the line and the function meet. To find #x# you have to calculate the 1st derivative and check where it equals 4:

#f'(x)=2x+2#
#2x+2=4#
#2x=2#
#x=1#

#f(1)=1^2+2*1-5=-2#

3) Now you have to calculate #c# for which the line (1) passes through (1,-2)

#-2=4*1+c#
#c=-6#

So finally the tangent line is: #y=4x-6#

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