Practice question: Find f(3) if12f(x) = x2 - 2:Solution: To evaluate f(3), we simply plug in the value of 3 for x in the expression:f(7) = 32.2 = 7.Find f(3)f'(3) represents the taking the first derivative of the expression and evaluating at x = 3:f'(x) = (2)3 (2-1) = (2)3f'(3) = (2)3 = 6Question: Find f(7) iff(x) = x2 + 7:f(7) :find f'(7)f'(7) = Practice question: Differentiate the following function:13y = 5x 3/2Solution: Using the power rule,dy/dx = y' = (3/2)(5x (3/2) - 1) = 15/10x 1/2 = 3/2x 1/2Question: Differentiate the given function:y= 2x4/3Instruction: enter each response as a fraction (i.e., 1/2, 3/4, 5/8, .)dy/dx= X

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ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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(1) A course repeater claims that his brother who did some Calculus at college years ago, but currently on some cough medication, believes that the first derivative of (2x² – 1)(x² + 3) [(2x? – 1)(x² + 3) 2х + |2x2 -1 х2 +3 4x 2x | f(x) -is f'(x) x? + 1 x2 + 1] x2 + 1 and (x² + 8)7 14х (x2 + 8)7 30х + 2 – 3x2] |(2 – 3x²)5 that the first derivative of g(x) is g'(x) = (2 — Зx?)5 lx² + 8 ' Using the product, qoutient and chain rules you learnt in Unit 7 of this Course, could you confirm whether his brother is right, wrong or a little tipsy.
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The revenue (in dollars) from the sale of x car seats for infants is given by the following function. R(x)=64x-0.020x² 0≤x≤3200 (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (B) Use the four-step process to find R'(x). (C) Find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and interpret the results. ... (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. 23 (Round to one decimal place as needed.) (B) R'(x) =
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DERIVATIVE In the following the symbol for the first derivative is dy/dx or Y’ and the symbol for the second derivative is d2y/dx2 or Y”, all of which are standard symbols. Y = X3 -2X2 +1 X -.333 0 .333 .667 1 1.333 1.667 Y dy/dx d2y/dx2 A function is given above. The table gives several pre-selected values of the independent variable (X). Use all of these to have enough to answer questions for this assignment. Calculate the Y value corresponding to each X value in the table. Write the Y value and its sign (+ or -) calculated in the cell below its X value. Pick any three of the X values and on a separate worksheet, show how you calculated its Y value. Use these X,Y pairs also if you chose to do the bonus option. Find the critical values among the given X values…
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