How do you show the line #y=6x-5# is a tangent to the quadratic equation #f(x)= 5x^2 - 14x + 15#?

1 Answer
Jim H
May 18, 2015

Show the line #y=6x-5# is a tangent to the quadratic equation #f(x)= 5x^2 - 14x + 15#

For #f(x)= 5x^2 - 14x + 15#, the slope of the tangent is given by :
#f'(x)= 10x - 14#..

The slope of #y=6x-5# is #6#. (#x=2)

Find the value of #x# at which the slope of the tangent is #6#.

Find the corresponding #y# value on the graph of #f(x)= 5x^2 - 14x + 15# . #(y=5(2^2)-14(2)+15)#

Finally, finish finding the equation of the tangent line at that point to see that it is, indeed #y=6x-5#.

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