Find an equation of the tangent line to the parabola y = 5x2 at the point P(2, 20) using this definition. %3D SOLUTION Here we have a = 2, and f(x) 5x, so the slope is as follows. !! f(x) - f(2) lim x - 2 m = X - 2 lim x - 2 %3D X - 2 5(x - 2) lim x - 2 %3D X – 2 lim 5 x - 2 ) = + 2 !! Using the point slope form of the equation of a line, we find an equation of the tangent line at (2, 20) is as follows. y-(D)-(D)(*-O) y - (D)x-(O). or Need Help? Read It

Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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Find an equation of the tangent line to the parabola y = 5x2 at the point P(2, 20) using this definition.
%3D
SOLUTION
Here we have a = 2, and f(x) = 5x, so the slope is as follows.
%3D
f(x) - f(2)
m =
lim
X - 2
= lim
x → 2
%3D
X – 2
5(x – 2)
lim
%D
X → 2
x – 2
= lim 5
X → 2
%3D
+ 2) -
%3D
Using the point slope form of the equation of a line, we find an equation of the tangent line at (2, 20) is as follows.
(D)-(0)(*-O)
y = (D)x-(D)
or
y -
Need Help?
Read It
||
Transcribed Image Text:Find an equation of the tangent line to the parabola y = 5x2 at the point P(2, 20) using this definition. %3D SOLUTION Here we have a = 2, and f(x) = 5x, so the slope is as follows. %3D f(x) - f(2) m = lim X - 2 = lim x → 2 %3D X – 2 5(x – 2) lim %D X → 2 x – 2 = lim 5 X → 2 %3D + 2) - %3D Using the point slope form of the equation of a line, we find an equation of the tangent line at (2, 20) is as follows. (D)-(0)(*-O) y = (D)x-(D) or y - Need Help? Read It ||
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