Calculus 10th Edition

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

Chapter 2 - Differentiation - 2.2 Exercises: 33

Answer

The derivative at the point $(0, -(\frac{1}{2}))$ is 0.

Work Step by Step

The function $-\frac{1}{2}+\frac{7}{5}x^3$ is the sum of "smaller" functions hence the overall derivative is the sum of the derivative of the smaller functions. The derivative of $-\frac{1}{2}$ is 0. The derivative of $\frac{7}{5}x^3$ is $(\frac{7}{5})(3)x^{3-1}$ which when simplified is equal to $\frac{21}{5}x^2$; hence, the overall derivative is $\frac{21}{5}x^2$. To evaluate the derivative substitute in the x-coordinate. Plugging in 0 gives us $(\frac{21}{5})(0)$ which is 0.
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