Determine an equation of the line tangent to the graph

Susan Munoz

Susan Munoz

Answered question

2021-11-11

Determine an equation of the line tangent to the graph of f at the point (a, f(a)) for the given value of a.
f(x)=1x+5
a=5

Answer & Explanation

Ched1950

Ched1950

Beginner2021-11-12Added 21 answers

From the Definition the tangent line is the unique line through (a,f(a)) with slope mtan. Its equation is
yf(a)=mtan(xa)
From the part a) f(5)=1100 according to this the slope of the tangent line is mtan=14. Replace x=5 in the given function to get
f(5)=15+5=110
Thus the tangent line with slope mtan and point P(5,110) is
y110=1100(x5)
y=1100x+120+110
y=1100x+320
Hence, the tangent line with slope mtan=1100 and point (5,110) is
y=1100x+320
Result: y=1100x+320

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