True False  Suppose a stationary police officer at point A sees you pass by at 5:10pm and his colleague 10 Miles down the road at point B sees you pass at 5:16pm. The speed limit is 65MPH between point A and point B. They can then prove you must have broken the speed limit at some point between A and B. You may assume that your position as a function of time is both continuous and dirferentiable everywhere. Your justification should cite a theorem.

Q: Find the equation of the normal line of f(x) = x⁴ + 2x at x = 1 using the limits definition.

A:

Q: Fermat's theorem states that if f has a relative extremum and if f'(x) exists, then f'(c) = 0.…

A:

Q: Suppose that an object moving along a straight line path has its velocity in feet per second at time…

A: Given :  Velocity as a function of time , v(t) = 29t-32+2 . To find : Displacement ∆x Solution:  Let…

Q: Every continuous function on a, b\, that has absolute extrema on endpoints, must have one .(a, b)…

A: b. False Consider a continuous function f (x) on [a, b], that has absolute extrema on the endpoints.…

Q: is there any linear independent functions with n – 1th continuous derivative g1, 92, ... , gn(with…

A:

Q: Find all points (x.y) where f(x.y) has a possible relative maximum or minimum. Then use the second…

A:

Q: Lat f be a continous and differentiable function. If f'(c) = 0 then c is a local maximum or local…

A: Answer

Q: Suppose we wish to compute the value of the continuous function f(x) for a given value of x. This is…

A: Solution: Explanation of equation (7.117) in the book: Given y=fx    ......(1) Now, (in the book)…

Q: 2. Let f(x) = Determine the exact location of any turning points. Use the second derivative to…

A: We can solve this as follows:

Q: Find all points (x,y) where f(x,y) has a possible relative maximum or minimum. Then use the second…

A:

Q: on. Find the method of moment estimate for 0

A: Given that sample size n = 4,  Y1 = 0.42, Y2 = 0.1, Y3 = 0.65, Y4 = 0.23

Q: True or FalseA 1. A Step-function is continuous at every point in its domain

A: Given: A step - function is continuous at every point in its domain. To write: The given statement…

Q: Aside from Extreme Value Theorem (EVT), there is another theorem behind optimization, the Fermat's…

A: This Fermat's theorem gives the emphasis at graphing of any function Consider a graph which is…

Q: Jaimie, a MAT student, claims that "For a continuous function f(x), defined on an interval [a, b],…

A:

Q: Determine intervals of convexity and inflection points of the function: f(x) = 2 * arctanx + In(1 +…

A:

Q: a) that has a relative maximum and is differentiable at 2. at 2. b) that hos a relotive maximmum at…

A: Here we draw the image for each questions.

Q: ) Suppose f (x) is continuous on [0, 2] and differentiable on (0,2). Suppose f (0) = 3 and f (2) =…

A: Use the concept of Roll's Theorem and Extreme Value theorem and solve the problems.

Q: 4.3. Show that the function f(x) = Ja² sin, if x 0, 0, if x = 0 is not of a bounded variation over…

A:

Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: To find two path of approach for the given function such that we conclude that no limit exist when…

Q: 1. If F(x) = - eta dt, find F(1) and F'(x).

A: If Fx=∫exe et2 dt, then to find F1 and F'x.

Q: If I have a continuous, smooth (no sharp points) function with 3 local maxima and 2 local minima,…

A: Since the function is continuous , with 3 local maxima and 2 local minima.the function will have 5…

Q: (a) The sales of a book publication are expected to grow according to the function S= 300000(1-…

A:

Q: Prove that constant function is differentiable at ever x ER.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: What is the isogonal trajectories family of curves x² - y² = a which intersects at an angle of ∅ =…

A:

Q: The sales of a book publicationare expected to grow according to the function S = 300000(1 -…

A: (i) The given function is S=3000001-e-0.06t. To calculate maxima dSdt=0. That is,…

Q: 4.On which condition is the function differentiable at a point? A) continuous at the given point B)…

A:

Q: Standing on a vast flat plain, an archer shoots an arrow into the air, at a speed of 50 ft/sec, and…

A: First draw the diagram . Then use the. Formula as v=u+at   Then find the time period .. Then  use…

Q: A vehicle accelerates from rest, and its speed is approximated by the following function: v(t) = 0.1…

A: The speed of the vehicle is approximated by the function vt=0.1t e30t2+50 Then the distance…

Q: Suppose /has a continuous derivative on the interval [0, 6]. Assume also that f' is increasing on…

A:

Q: A vehicle accelerates from rest, and its speed is approximated by the following function: v(t) = 0.1…

A: Consider the given velocity function and the sketch for the velocity function v(t) for t = 80 till t…

Q: Aside from Extreme Value Theorem, there is another theorem behind optimization, the Fermat’s…

A: Since interval is open and c in the interval this excludes c being one of the interval limits.   If…

Q: If f '(x) > on an open interval extending left from c andf (x) < on an open interval extending right…

A:

Q: Given the piecewise function f(x) = Why is f not differentiable at x = 5? Of is continuous at x = :5…

A: This question is based on continuity of function.

Q: While studying for Test 2, Miguel says to his classmates "Fermat's Theorem (page 5 in Lecture Notes…

A: According to Miguel's statement Fermat's theorem is " For a function f(x), if f'(x)=0, then f has…

Q: let f(x)= 5x2. Show that f(3+h)=5h2+30h+45. Then show that  (f(3+h)-f(3))/h=5h+30 and compute the…

A: Compute: f(3+h)

Q: Find the largest open interval using the tools of calculus where the function is changing as…

A:

Q: Express the limit as a definite integral on the given interval.

A:

Q: 7. Where is f(x.y)= continuous? Do not just write an answer, show your work or give any necessary…

A:

Q: question. sf continuous at x = - 3? AY 5- 4- 3- 20 -5 -4 3 -2 -14 123 4 5 -2- -3- -4- -5-

A:

Q: Suppose that we roll a balanced four-sided die twice. Let Y be the maximum of the two numbers. Type…

A: If a four sided die is rolled then total possible outcomes = 4 and each outcomes are equally likely…

Q: A tank contains 100 gal of brine in which 50 lb of salt is dissolved. Brine containing 2 lb/gal of…

A: 1 st we will make differential equation for amount of salt and then solve it to get amount of salt

Q: What is the value (i.e. what do we learn) from using the Wronskian on a set of functions?

A: Let F = { f1, f2, f3, ...fn} be the set of functions. 1. If W(f1, f2, f3,...fn) =0 Then we say…

Q: Use the first derivative test to determine the local extrema, if any, for the function f(x) = 3x -…

A: Answer

Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: The given question is related with limits. Given that fx , y = 3y9x2 + 4y2 . We have to find two…

Q: Answer the following True or False: For every continuous nonlinear function, you can find a value of…

A: To states whether true or false. For every continuous non linear function, there is a value of x…

Q: This exercise is about limits at infinity. The population of a certain species living in certain a…

A: Solve the following

Q: What are the Continuity Conditions?

A: When a graph has no holes, no asymptotes or the graphs that does not have breaks are called…

Q: 1 . Let f(r) 2r + 1

A:

Q: Sketch the graph of a function f that is continuouson [1, 5] and has the given properties. Absolute…

A: Given: The function is continuous on [1,5] The absolute minimum is at 2 The absolute maximum is at 3…