Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.1 Exercises - Page 103: 34



Work Step by Step

Function: $f(x)=2x^2$ Line: $4x+y+3=0$ 1. Find the slope $m$ of the given line by putting it into point-slope form: $y=-4x-3$, $m=-4$ 2. Take the derivative of the function: $f'(x)=4x$ 3. Set $f'(x)$ equal to $m$ and solve for the $x$-coordinate: $4x=-4$ $x=-1$ 4. Plug in $x$ from part 3 into $f(x)$ to get the $y$-coordinate: $y=f(-1)=2(-1)^2=2$ Point: $(-1,2)$ 5. Plug the slope $m$ and the point into the point-slope formula $(y-y_{1})=m(x-x_{1)}$: $(y-2)=-4(x+1)$* *In most cases point-slope form is sufficient. If not, simply convert into whatever form your professor deems acceptable.
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