Answered: f(x) = 1.5x? – r + 3.7

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.1: Functions And Function Notation

Problem 8TI: Using Figure 7, solve f(x)=1 .

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Question

Find the derivative of the function using the definition
of derivative. State the domain of the function and the domain of
its derivative.

Expert Solution

Step 1

we have to find the derivative of the function

$f (x) = 1.5 x^{2} - x + 3.7$

we have to write the domain of the function and the domain of its derivative.

Step 2

we will first find the derivative of f(x)

$f (x) = 1.5 x^{2} - x + 3.7 f' (x) = \lim_{h \to 0} \frac{f (x + h) - f (x)}{h} f' (x) = \lim_{h \to 0} \frac{1.5 {(x + h)}^{2} - (x + h) - f (x)}{h} f' (x) = \lim_{h \to 0} \frac{1.5 x^{2} + 1.5 h^{2} + 3 x h - x - h + 3.7 - 1.5 x^{2} + x - 3.7}{h} f' (x) = \lim_{h \to 0} \frac{1.5 h^{2} + 3 x h - h}{h} f' (x) = 3 x - 1$

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