Chapter 10.2, Problem 4E

Chapter
Section
Textbook Problem

# Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.4. x = t , y = t2 − 2t; t = 4

To determine

To find: The equation of the tangent for the parametric equations x=t and y=t22t.

Explanation

Given:

The parametric equation for the variable x is as follows.

x=t (1)

The parametric equation for the variable y is as follows.

y=t22t (2)

Calculation:

Differentiate the parametric equation x with respect to t.

x=tddtt=12t

Apply differentiation formula (ddx(u)=dx2u) in the above equation.

Differentiate the parametric equation y with respect to t.

y=t22tdydt=2t2

Write the chain rule for dydx.

dydx=dydtdxdt=(2t2)(12t)=(2t2)2t (3)

Substitute for (2t2) for dydt and (12t) for dxdt in the above equation.

Write the equation for tangent

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