## Thomas' Calculus 13th Edition

Published by Pearson

# Chapter 3: Derivatives - Section 3.1 - Tangents and the Derivative at a Point - Exercises 3.1 - Page 108: 19

#### Answer

$f'(1)=-1$

#### Work Step by Step

To find the slope of a function at any given point, all one has to do would be to look for the value of the derivative function at the same x value. Given that $f(x)=5x-3x^2$, then the derivative function by the power rule will be $f'(x)=5x^{1-1}-3(2)x^{2-1}=5-6x$ As such, the slope at the point $x=1$ would be $f'(1)=5-6(1)=-1$

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