x(x2 – 1) x2 +1 63. GU Let h(x) and the increasing/decreasing behavior of f. Sketch a plausible graph for f itself. and suppose that f'(x) = h(x). Plot h and use the plot to describe the local extrema

Q: 6(x² + 3) ((x – 3)(x + 3))³ 1 -2x f(x) = f (2) = f (x) = (x – 3)(x + 3) ((г — 3)(х + 3))?

A: Since, the numerator is a constant 1, so, the graph has only one horizontal asymptote which is the…

Q: 7. Let f be a function that has first derivative f /(x) = +2 and second derivative f"(x) = 2-2++2.…

A:

Q: 2. Graph the function f (x)= x+ Vlx\ . Zoom in repeatedly, first toward the point (-1, 0) and then…

A: Note: There are multiple questions. No specific question has been asked.So, We will solve the first…

Q: find the derivative of f(x) = x-3/3x+4 using the limit definition of the derivative. then state the…

A: Consider the given function as fx=x-33x+4. The limit definition of the derivative of a function fx…

Q: (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is…

A: Given function is fx=x2-6x+5. Critical numbers of a function is the point where its first derivative…

Q: of these functions has a fixed point. What happens when you iterate them 3. Consider the real-valued…

A: Since we know that, fixed point is the intersection point of y=x and y=f(x), it means graph of line…

Q: Let g be a function that is defined for all x, x # 2, such that g(3) = 4 and the derivative of g is…

A: Critical points of the function are the point either the derivative is not defined or derivative is…

Q: Consider the continuous function h with h' (x) = ln(x2)+4/2x1/2 3.1 Find and represent the domain…

A:

Q: Suppose a tour guide has a bus that holds a maximum of 86 people. Assume his profit (in dollars) for…

A: Solve the following

Q: Consider the function h(x) = 2 - 4x2 + 10. Use the second derivative test to find the r-coordinates…

A:

Q: 10- Continuity of the function f(x){*-5 -1<x<2 x² -1 2< x< 3 at x=2?

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

Q: F(X)

A: y = f(x) is continuous at x = a  only if following properties are satisfy : (1)  f(a) exists . (2)…

Q: Using the (e- 6) definition, show that f(x) = 3x – 1 is continuous at point x = 1.

A:

Q: 81. A function y = f(x) is increasing on the interval (0,5). What conclusions can you draw about the…

A: If a function is an increasing function then this means when the value of the variable x increases…

Q: 1. Given f(x)= (a) Show that f'(x)= 2(x² -16) 3x by using the quotient rule. Hence, find all 11 the…

A:

Q: (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is…

A: Given: fx=-3x2-4x-2

Q: ecos-1 x if x 1

A: If a function has to be continuous  then it must to follow below Left hand limit = Right  hand limit…

Q: 2. f(x) = is a continuous function but it is discontinuous at x = 3. Explain why X - 3 this is not a…

A:

Q: 1) If possible, give an example of where a function is differentiable at a point but not continuous…

A:

Q: Let f(x) = 5x? + x + 9 Use the second derivative test to find any local maxima and minima. First,…

A:

Q: 3. Determine the x interval(s) on which the function is increasing.

A: From the given Figure, it is observed that the graph of function has local maximum at x=-4  and…

Q: Let f (x) = 2x3 + 18x2 + 63.Use the First Derivative Test to determine the relative extreme values…

A: Given:

Q: 6. Find the absolute extrema of the function on the closed interval given: f(x) = 2x/2 – x; [ –2,1]

A: Pue derivative zero, if value lie in interval then put in function for maxima and minima

Q: Consider the piecewise function 1 3.x if x < -2 f (x) = ax2 + 2x + b if – 2 < x Where a and b are…

A:

Q: (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is…

A: f(x)=x2+6x+10

Q: (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is…

A: a. xxTo find the critical points we will have to solve the question:    f'(x) = 0 So first we want…

Q: 3) Let f(x) = 3x – 1. Use the limit definition of the derivative to find f'(x).

A:

Q: 2. Use the limit definition of derivatives to find the expression for f'(a) for the function 1 f(x)…

A: Here ,               We have given a function now we have to solve it by using definition of limit…

Q: Sketch the graph of f(x) = x lxl. Then show that f '(0) exists.

A: A function is a relation which maps each value in domain to exactly one value in range.  For a…

Q: Let g be a function that is defined for all x, x 2, such that g(3) = 4 and the derivative of g is x²…

A: The interval where second derivative of function is positive, is the interval where the function is…

Q: 10. Find a function f such that f'(x) =r' and the line 4x - ļy = 3 is tangent to the graph of f. %3D

A:

Q: Determine the intervals of concavity for the function f(x)=e^(-x)- e^(-(-3x).You must use exact…

A:

Q: 5. Let f(x)= x . arccos x. Find f'(-/3/2) ||

A:

Q: 6. Find the length of the curve given by the graph of the function f(x) = x/x, for x in [1,4].…

A:

Q: 2. Let f(x) =- 3-2x Use the definition of the derivative to find f'(x). Show complete work,…

A: The given function is f(x)=x23-2x.

Q: Find the constant a such that the function is continuous on the entire real line. (8x?, lax – 6, x2…

A: Given function f(x) = 8x2-x≥1ax-6, x&lt;4we find constant 'a' such that the function is continuous…

Q: Find all points where the function f(x) = |x|p with p > 0 is differentiable. How does your answer…

A:

Q: Consider the function f(x) = 2/x + 2 on the interval [4, 8]. Find th function on this interval.

A:

Q: Q3. Determine whether the function is continuous at x=1 or not (x² - 1 x = 1 f(x)=x-1 2, x = 1

A:

Q: Consider the function y = -x3 + 3x² – 2. a) Find the critical points. b) Use the 2nd Derivative Test…

A:

Q: 4. Find the intervals of concavity for the function f(x) = e-/3. Identify any inflection points.

A: use double differentiation =0 to find inflection points and concavity

Q: 46. Let f(x) = x³ - 4x² . Find the points on the graph of f where the tangent %3D line is…

A: 46. The given function is fx=x3-4x2. Differentiate fx with respect to x. f'x=ddxx3-4x2=3x2-8x Now,…

Q: Find all critical numbers for the following function. Then use the second-derivative test on each…

A:

Q: Let P=(x,y) be a point on the graph of y=square root of x a) Express the distanced d from P to the…

A: Please refer to the image below.

Q: Use the graph of the function to estimate the interval on which the function is decreasing. y Enter…

A: Given : To find : Interval on which the function is decreasing. If the value of function fx…

Q: Q20: . Suppose that f(x) is continuous and differentiable on the interval [0,6], that f(6) = -7 and…

A: Given that the function “f (x)” is continuous and differentiable on the interval [0, 6] that, f (6)…

Q: Q4: Use the limit definition to compute the derivative, f'(x), for 2 1.F(x) = x3 2.F(x) = Vx³ – x

A:

Q: 6x + 7, on the Find all absolute and relative extreme values of the function f(x) interval [1, 4].…

A:

Q: Show that the function f(x) = |x-3| is not differentiable at x = 3.

A:

Q: 9. Given the function f(x) 3x*-4x2 +2, use the first and second derivative tests to find: a) the…

A: