This problem investigates the derivative of the absolute value function. Recall that we define the absolute...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
This problem investigates the derivative of the absolute value function. Recall that we define the absolute value as: |x| { (a) In the space provided, draw a graph of the function f(x) = |x|. 3- = x f'(x) = -I + -3 -2 −1 if x ≥ 0, if x < 0. 2- 1. + 1 2 3 (b) Using your graph from part (a), and your understanding of the derivative as the rate of change/slope of the tangent line, find the derivative function f'(x) of the above function f(x)= x, for r not equal to 0 (fill in the blanks): if x > 0, if x < 0. (c) But what about f'(0)? It is not so clear from the picture even how to draw a tangent line to the function at the origin. So let's try to compute f'(0) by first looking at the corresponding lefthand and righthand limits of the difference quotient. i. Compute limh→0+ f(0+h)-f(0). Hint: use the piecewise definition of f(x) given above. h ii. Compute limh→0- ƒ(0+h)-f(0) iii. What do your answers to parts (i) and (ii) tell you about f'(0)? Please explain. This problem investigates the derivative of the absolute value function. Recall that we define the absolute value as: |x| { (a) In the space provided, draw a graph of the function f(x) = |x|. 3- = x f'(x) = -I + -3 -2 −1 if x ≥ 0, if x < 0. 2- 1. + 1 2 3 (b) Using your graph from part (a), and your understanding of the derivative as the rate of change/slope of the tangent line, find the derivative function f'(x) of the above function f(x)= x, for r not equal to 0 (fill in the blanks): if x > 0, if x < 0. (c) But what about f'(0)? It is not so clear from the picture even how to draw a tangent line to the function at the origin. So let's try to compute f'(0) by first looking at the corresponding lefthand and righthand limits of the difference quotient. i. Compute limh→0+ f(0+h)-f(0). Hint: use the piecewise definition of f(x) given above. h ii. Compute limh→0- ƒ(0+h)-f(0) iii. What do your answers to parts (i) and (ii) tell you about f'(0)? Please explain.
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
This problem investigates the sensitivity of the prices of bonds carrying differing coupon rates to interest rate changes. Bonds K and L both have a face value of $1000 and 15 years remaining until...
-
Use the continuity of the absolute value function to determine the interval(s) on which the following functions are continuous. f(x) = |x 2 + 3x - 18|
-
Use the continuity of the absolute value function to determine the interval(s) on which the following functions are continuous. x + 4 g(x) x 4 ||
-
Sarah works for an accounting company. She has a lot of administrative procedures to follow and little flexibility in the way she performs her daily work. Sarah's job has a high level of _____....
-
Why does the value of a share of stock depend on dividends? (150 words)
-
The following data are the number of spelling errors detected for every 1000 words on a news Web site over 20 weeks. (a) What control chart is most appropriate for these data? (b) Using all the data,...
-
Wayne Robichaud, Attorney, P.C., began the year with total assets of \($127,000\), liabilities of \($78,000\), and stockholders equity of \($49,000\). During the year the business earned rev enue of...
-
A woman made 10 annual end-of-year purchases of $1000 worth of common stock. The stock paid no dividends. Then for 4 years she held the stock. At the end of the 4 years she sold all the stock for...
-
Linda Company began making cosmetics in April 2021 using a single-step process. Linda incurred P21,000 for materials and P24,320 for conversion during the month. There were 14,000 pints of cosmetics...
-
Refer to the North Valley Real Estate data, which report information on homes sold during the last year. For the variable price, select an appropriate class interval and organize the selling prices...
-
Jiffy Co. expects to pay a dividend of $3.00 per share within one year. The current price of Jiffy common stock is $60 per share. When Jiffy issues new stock, the IPO cost is $3.00 per share. If...
-
What are some key challenges in economic development that developing countries facing in the midst of Covid 19 pandemic? How can these challenges be addressed? What are the constraints to address...
-
Households Product Markets Factor Markets Fams Refer to Figure 2-13. What is represented by the arrow from the firms to the factor markets?
-
Businesses seeking higher profits and resource suppliers seeking higher incomes lead to changes in the allocation of resources among different firms and end up with?
-
In today's global economy, many companies are looking for ways to cut costs. One of the major costs for companies is shipping goods overseas. To reduce this, firms actively seek foreign direct...
-
You want to buy a $35,000 car today, but you don't have the cash to buy it. The dealership is offering to loan you the money at 7% interest with payments made monthly for the next five years. If you...
-
Donna is a 20% owner in an advertising agency named Bright Ideas ("BI"). BI is a Subchapter S corporation. The company reported ordinary business income for the year of $150,000. Donna received a K-1...
-
Which of the following gives the range of y = 4 - 2 -x ? (A) (- , ) (B) (- , 4) (C) [- 4, ) (D) (- , 4] (E) All reals
-
A hot-air balloon is flying at a height of 600 feet and is directly above the Marshall Space Flight Center in Huntsville, Alabama. The pilot of the balloon looks down at the airport that is known to...
-
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 5 k-1 5. 5 4 k=1
-
Determine the quadratic function whose graph is given in the figure. YA 50 (0, 24) -2 8 -10F Vertex: (4, -8)
-
What are the major elements of risk assessment?
-
How does an organization go about identifying, measuring, and prioritizing risks? Who is responsible for the assessment of risk in an organization?
-
What is risk? How does management generally perceive the dimensions of risk?
Study smarter with the SolutionInn App