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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
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 = x2 at (– 2, 4) is y – 4 = 2x(x + 2).

To determine

Whether the statement, “An equation of the tangent line to the parabola y=x2 at (2,4) is y4=2x(x+2)” is true or false.

Explanation

Formula used:

The equation of the tangent line at (x1,y1) is, yy1=m(xx1) (1)

Where, m is the slope of the tangent line at (x1,y1) and m=dydx|x=x1.

Calculation:

The derivative of y is dydx, which is obtained as follows.

dydx=ddx(y) =ddx(x2)=2x

Therefore, the derivative of the function y=x2 is 2x_

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