Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 4 - Calculating the Derivative - 4.1 Techniques for Finding Derivatives - 4.1 Exercises - Page 207: 32


$$y=-31 x+24$$

Work Step by Step

Since $$y=-3 x^{5}-8 x^{3}+4 x^{2},\ \ \ x=1 $$ Then $y(1)=-7$ Finding the derivative of the function$$ \frac{d y}{d x}=-18 x^{4}-24 x^{2}+8 x $$ Then slope given by \begin{align*} m&=\dfrac{dy}{dx}\bigg|_{1}\\ &=-18(1)^{4}-24(1)^{2}+8(1)\\ &=-31 \end{align*} Hence the equation of tangent given by \begin{align*}y-y_{1}&=m\left(x-x_{1}\right) \\ y-(-7)&=-31(x-1)\\ y& = -31 x+24 \end{align*}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.