What is the equation of the tangent to #y=5x^2-7x+4# at the point #(2, 10)#?

1 Answer
Mia
Nov 25, 2016

#y=13x-16#

Explanation:

The equation of the tangent is determined by finding the slope at
#" "#
the point #x=2#
#" "#
The slope is determined by differentiating #y# at #x=2#
#" "#
#y=5x^2-7x+4#
#" "#
#y'=10x-7#
#" "#
#y'_(x=2) =10(2)-7#

#" "#
#y'_(x=2) =20 - 7=13#
#" "#
The equation of the tangent of slope #13# and passing through the
#" "#
point #(2,10)# is:
#" "#
#y-10=13(x-2)#
#" "#
#y-10=13x-26#
#" "#
#y=13x-26+10#
#" "#
#y=13x-16#

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