   Chapter 2.R, Problem 11TFQ

Chapter
Section
Textbook Problem

# Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.An equation of the tangent line to the parabola y = x 2 at ( − 2 , 4 ) is y − 4 = 2 x ( x + 2 ) .

To determine

To state:

Whether the given statement,"An equation of the tangent line to the parabola y= x 2 at(-2,4)is y4=2x(x+2) " is true or false.

Explanation

Equation of parabola is y=x2

To find the slope of tangent at =(-2 , 4), we need to find the derivative of curve at that point. Differentiating the equation of parabola with respect to x we have

dydx=2x

Slope at point x1 , y1=(-2 , 4) becomes dydx=2x1</

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