Problem The graph of a function r = f (t) is shown below. *=f(t) -2 A curve C in the ry-plane is defined from the set of parametric equations r(t) = f(t), y = t2 + 4t, - 3

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Chapter8: Polar Coordinates And Parametric Equations
Section8.FOM: Focus On Modeling: The Path Of A Projectile
Problem 6P: Shooting into the Wind Suppose that a projectile is fired into a headwind that pushes it back so as...
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y=t^2+4t

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Problem
The graph of a function r = f (t) is shown below.
*=f(t)
-2
A curve C in the ry-plane is defined from the set of parametric equations r(t) = f(t), y = t2 + 4t, - 3<t< 4.
Find the equations of all horizontal tangent lines to C and state the coordinates (r, y) where they occur.
B.
Find the equation of the tangent line to C at (2, 9) = (1, 12).
dr
Explain whether r= f(t) could be a solution to the differential equation
dt
2 +t for -3 <t< 4.
C.
Transcribed Image Text:Problem The graph of a function r = f (t) is shown below. *=f(t) -2 A curve C in the ry-plane is defined from the set of parametric equations r(t) = f(t), y = t2 + 4t, - 3<t< 4. Find the equations of all horizontal tangent lines to C and state the coordinates (r, y) where they occur. B. Find the equation of the tangent line to C at (2, 9) = (1, 12). dr Explain whether r= f(t) could be a solution to the differential equation dt 2 +t for -3 <t< 4. C.
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