check uniquness and existance for fixed point while f(x)=(2x+1)^-3 in [1,2]

Q: Let f(x)=x² -3x+5. Show that the average rate of change of f (with respect to x) on an arbitrary…

A: Average rate of change = (f(b)-f(a))/(b-a) Instantaneous rate of change =f'(a+b/2)

Q: The second derivative test is used to distinguish between maximum and minimum points by determining…

A:

Q: ) The tangent line to y = f(x) at (-5, 2) passes through the point (-7, -5). Compute the following.…

A:

Q: OFind the eguation of the tangent line for f(x) = 6x²-3x +a when x= 5. You may problem. use…

A:

Q: Find the equaiton of the tangent line for the function f(x)=x+3/x-3 at the point (4,7).

A: We find f'(x) using the quotient rule.

Q: Use Second Derivative Test to find the location of all local extrema for f(x) = 2x³ + 15x² + 24x – 3

A: We Know that The second derivative may be used to determine local extrema of a function under…

Q: Find equations of the two tangent lines to the graph of f(x) = x² that pass through the point (-1,…

A: Given that f(x)=x2 To find two tangents that passes through (-1,-3)

Q: 2. f(x) = 3. g(x) = 5 In x – 2* 4. g(x) = 4x³ log, x

A: To find the derivative of the given function. 2). Given function is fx=x2ex. Quotient rule of…

Q: yこ(3x)2 - 5c0s x : 1(3x) |(3x)" -Scosx

A:

Q: Find the relative extrema of f(x) = 8+ 126x – 7x2 using both first and second derivative tests. f…

A: If second derivative is less than zero then there is relative maxima.

Q: 6. A rancher wants to fence off a rectangular corral with an area of 4050 sq. yds next to a river.…

A:

Q: Use the First Derivative Test to locate the x-value of all extrema. Classify if it is a relative…

A:

Q: 1. Use the limit definition of derivative (no shortcuts!) to find the derivative of f(x) = 3x² + 2x.

A: The formula for derivative of function f(x) using limit is given by:…

Q: The slope of the tangent line to the graph of the function y = 2x3 at the point (2, 16) is lim2"…

A:

Q: Use the first derivative test to locate all local extrema for 3 f (x) = -x'+ = -x' +- x +18x.

A: Explanation of the answer is as follows

Q: Use second derivative test, If x3 f(x) = 25x + 5 then f(x) has a 3 local maximum at the point x = -3…

A:

Q: 1. f(x)= Vx3 + 2x² + 3 2. f(x) = (6x – 7)(2x + 3)

A: To find the second derivatives of the given functions.

Q: Find equations of the two tangent lines to the graph of f(x) = 2x² that pass through the point (1,…

A: Given:- f(x) = 2x2  To find:- Equation of tangent lines passes through (1, -6)

Q: Find the local maximum and minimum values of f using the Second Derivative Test. If the Second…

A:

Q: (8 points) Find the slope of the line tangent to the graph of 1 f (x) = 2x* – 32x + 17x2 – 9x + 4 at…

A:

Q: Use the First Derivative Test to locate the x-value of all extrema. Classify if it is a relative…

A:

Q: oFind the derivative: (show all 1. f(x) = 2xe-3x chou

A:

Q: 9) Use the second Derivative Test to find all relative extrema. f( x) = - (x + 2)°(x – 4)?

A: Find f'(x) and solve for x by putting f'(x)=0.

Q: Use Intermediate Value Theorem to show that the equation

A:

Q: Find the co-ordinates of the minimum turning point for the function f(x)= 2x² + ± 4 Using the second…

A:

Q: - Find the point of tangency and the equation of the tangent line passing through the point p(-4,-2)…

A: Given: Now, f'(x)=-3-2x. At (-4, -2), slope = -3-2(-4) = 5. So, the equation of the tangent line is…

Q: Find local maximum or local minimum of f(x) = - sin 2x -x defined on 2'2

A:

Q: Find the equation of a tangent line to the graph of f(x) = x² – 2X at (-2,8). TYPE IN THE EQUATION…

A:

Q: The tangent line to y = f(x) at (-1,-8) passes through the point (-7,5). Compute the following a.)…

A: The tangent line to y=f(x) at (-1,-8) passes through the point (-7,5)

Q: Use Second Derivative Test to find the location of all local extrema for f(x)=2x³+21x²+36x-1

A: Local extrema.

Q: Use second derivative test, If f(x) = - 4x + 10 then f(x) has a local maximum at the point 3 %3D O r…

A: here we need to find the point at which the function has a local maxima. the solution is following.

Q: Find an equation of the tangent line to the graph of function f(x): 3 %3D x+5 at the point (2, ).…

A:

Q: find the derivative of f(x) = (x²+4)(3x³ – 2x) at the point x = - 3[ use product rule] В I !!

A:

Q: %3D Find the second derivative of f(x) = 3e*-8e-6x

A: We have to find the second derivative of the function: fx=3e5x-8e-6x We know the formula of…

Q: (A) Find the absolute maxima and minima for y 4x +1 over 3 - [-V5, V5]. (B) Use the second…

A:

Q: Give an example of a function that is defined for all real numbers, is continuous everywhere, but…

A:

Q: 2. Find the derivative of f(x) = -4x2 + 3x + 2 from first principles (i.e. the limit definition of a…

A:

Q: Find the equation of the tangent line to the function f(x) 8vx - 4 at the point (64, 60). Provide…

A: Calculate the slope of the given function;

Q: How to find stationary points for f(x) = x^2-6x^2+9x and their local max or local min

A:

Q: Find the equation of the tangent and normal line of the function f(x) = \sqrt(2x−1)​ at the point…

A:

Q: Joha Find the derivative of the 1 1- f(x)= 2x+3

A:

Q: f(x) = (6x – 7)(2x + 3) %3D

A: Given  f(x)=(6x-7)(2x+3)

Q: 4. Find the maxima/minima of f(x) = x³ – x using both 1st and 2nd derivative test.

A: Consider the function: fx=13x3-x. Find maxima, minima.   Find f'x by applying axn'=anxn-1.…

Q: Find the critical points and extreme values of the function below. Extreme values must by verified…

A: Given,         y=x3-12x+2

Q: 27. Find the derivative of f(x) = (1 + 2x²)(x – x²) in two ways: by using the Product Rule and by…

A: Derivative of the function f(x) is given by

Q: Use the second derivative test to find the extreme values of the function f(z) = z-3z2-24z

A:

Q: Find the equation of the tangent line to the function f(x) = 8/x - 2 at the point (64, 62). Provide…

A: To determine the equation of the tangent in the form y =mx+b

Q: Find the local maximum and local minimum values of f using both the First and Second Derivative…

A: