Question: (a) What does it mean for f to be differentiable at a? (b) What is the relation between the differentiability and continuity of a function?

(a) What does it mean for f to be differentiable at a?
(b) What is the relation between the differentiability and continuity of a function?
(c) Sketch the graph of a function that is continuous but not differentiable at a = 2.

Step by Step Solution

★★★★★

3.59 Rating (170 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a A function f is differentiable at a number ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

M-C-L-D (246).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

(a) What does it mean for f to be continuous at a? (b) What does it mean for f to be continuous on the interval (-, )? What can you say about the graph of such a function?

What is foreign exchange risk? What does it mean for an FI to be net long in foreign assets? What does it mean for an FI to be net short in foreign assets? In each case, what must happen to the...

What does it mean for a company when they discover that their product has a High BDI but low CDI? What about a low CDI and Low BDI?

(a) What does it mean for f to be differentiable at a? (b) What is the relation between the differentiability and continuity of a function? (c) Sketch the graph of a function that is continuous but...

I need some help, can someone explain to me the following questions; Discuss the derivative of f'(a). Discuss two ways of interpreting this number. What does it mean for f to be differentiable at a?...

(a) What does it mean for f to be differentiable at a? (b) Sketch the graph of a function that is continuous but not differentiable at a = 2.

11. Find f ' ( x ) if f ( x ) = ( x3 + 2x + 4) 2. A. 12 (3x2 + 2) ( x3 + 2x + 4 ) B. 2x2 + 4x + 8 C. 2(3x2 + 2 ) ( x3 + 2x + 4 ) D. 3x2 + 2 12. What is the derivative of h(x) = (3x2 + 4)(2x - 3)? A....

1. [-/3 Points] DETAILS LARCALC9 3.2.005. Find the two x-intercepts of the function f and show that f '(x) = 0 at some point between the two x-intercepts. f( x ) = x2 - 2x - 15 ( x, y ) = ( (smaller...

Kindly show your steps pletely correct. 1. A production function is given by f(K. L) - L/2+VK. Given this form. MP - 1/2 and MPk - JR. (a) Are there constant returns to scale, decreasing returns to...

Consider the function f(x) = x2 - x - 30. Use a graphing utility to graph f, the secant line, and the tangent line. (a) Find the equation of the secant line joining the points (-4, -10), and (6, 0)....

The relaxation time is =1 s for a sample of bacterial DNA molecules having a molecular weight of 10 8 g/mol in a concentrated solution. Given that the elastic moduli of concentrated DNA solutions of...

A project requires a net investment of $450,000. It has a profitability index of 1.25 based on the firm's 12 percent cost of capital. Determine the net present value of the project.

An enrolled iris template: 1 0 1 0 1 0 1 1 0 1 1 0 0 1 0 1 A probe iris code: 1 1 1 0 1 1 1 1 1 1 0 1 0 1 0 1 Given a threshold 0 . 3 5 ( 3 5 % ) , do they match? Question 1 options: A ) Yes. B ) No...

Comparative balance sheets for Erisa Magambo Company are presented below. Additional information:1. Net income for 2012 was $125,000.2. Cash dividends of $60,000 were declared and paid.3. Bonds...

Here are comparative balance sheets for Syal Company. Additional information:1. Net income for 2012 was $103,000.2. Cash dividends of $45,000 were declared and paid.3. Bonds payable amounting to...

Joint-cost allocation, insurance settlement Quality Chicken grows and processes chickens. Each chicken is disassembled into five main parts. Information pertaining to production in July 2009 is:...

Joint-cost allocation, process further. Sinclair Oil & Gas, a large energy conglomerate, jointly processes purchased hydrocarbons to generate three non-saleable intermediate products: ICR8, ING4, and...

Joint products and byproducts (continuation of 16-16). Quality Chicken is computing the ending inventory values for its July 31, 2009, balance sheet. ending inventory amounts on July 31 are 15 pounds...

How many atoms of hydrogen are in 100 g of hydrogen peroxide (H 2 O 2 )?

Shown is a graph of the global average temperature T during the 20th century. Estimate the following. (a) The global average temperature in 1950 (b) The year when the average temperature was...

Sketch the region in the plane defined by each of the following equations or inequalities. (a) max{x, 2y} = 1 (b) 1 max {x, 2y} 1 (c) max{x, y 2 } = 1

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = (x 3)...

please reply if you can answer all the questions. 1. What is the present value of a 15-year annuity that pays $50 per year, assuming 12% annual interest rate ? _________ 2. Assume you currently have...

Complete a simple regression analysis using mileage to predict selling price. Simple regression: 1. Describe dataset 1. Cross sectional ortimeseries 2. Types of variables 3. Dene explanatory and...

3. A professor wants to research about correlation between their students' performance and time spent on watching web-series. The professor asked 7 students about how many hours per week they spent...