Let L(x) = ln(x² + 4x + 14) in the interval [-10,10]. What are the absolute extrema of L(x) in this interval?

Q: (₁ Find the absolute extrema of the function on the closed interval. ƒ(x) = x³ − 12x + 1, [-3,1]

A: An absolute extrema of a function in a given interval is the point at which a maximum or minimum…

Q: Explain why the function g(x) = ln(4-x2) + square root of x+1 is continuous at every number in its…

A: Consider the given function g(x). The function g(x) is the sum of two functions f(x) and h(x).First…

Q: find the absolute maximum and absolute minimum values of ƒ over the interval. ƒ(x) = (4/x) + ln x2,…

A: Given,

Q: use the second derivative test to find the local exterma of the function  f(x) =x3-9x2-48x+72 on R

A:

Q: 5. Find the absolute extrema of f(x) = x’ + 3x – 9x + 4 on the closed interval [-4, 0].

A: The given function fx=x3+3x2-9x+4

Q: Find the local minima/maxima of -x + ln x if it exist

A: fx=-x+lnx Differentiating with respect to x, we get f'x=-1+1x Now to find critical values, solve the…

Q: ln(x) is just defined for x greater than 1. Select one: True False

A:

Q: Vx + 2 Determine where f(x) = is continuous. In(3x – 5)

A:

Q: Determine the intervals where the function f (x) = x ln x (x 7 0) is increasing and where it is…

A:

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x ln…

A: Now differentiating with respect to x, we get

Q: use the second derivative test to find the local exterma of the function f(x) =x3 -9x2-48x+72 on R

A:

Q: Find the absolute extrema of the function on the closed interval.                          h(x) = 5…

A:

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x2 ln…

A:

Q: Use mathematical induction to prove that the derivative of f (x) = x^n equals nx^(n-1) whenever n is…

A: Given: P(n) be the statement derivative of f(x)=xn is equal to nxn-1, where n is a positive integer.

Q: 1. f(x) = x² +x – 1 for all values of x -

A:

Q: Find the absolute extrema of f(x) = x3 +5x2-8x+2 on the interval [−1, 2].

A: Given function is fx=x3+5x2-8x+2 ; x∈-1, 2

Q: Find the absolute extrema of f(x) = 6x + 4 + on the closed interval [1, 6). Show all work.

A: Absolute extrema at x=2 and 6..

Q: Apply the Mean Value Theorem for the function f(x) = 2 ln(4x + 7) over the interval [1,3]. Show your…

A:

Q: Example: Use the Secant method to estimate the root of f(x) = e-x-x. Start with initial estimates…

A: To use secant method to estimate the root of fx=e−x−x

Q: 1. Find the absolute extrema of f (x) = x* - 8x² + 3 on the interval [-1,3].

A: Absolute extrema on a closed interval lies on end points or at f'(x) = 0 So first we have to…

Q: Find the absolute extrema of f (x) = 2x – 3x² – 12x +1 on the interval [-3,3].

A: fx=2x3-3x2-12x+1 Differentiating with respect to x, we get f'x=23x2-32x-121+0=6x2-6x-12 Now to find…

Q: 8. Find the absolute extrema of f(x) = 6x + 4 + on the closed interval [1, 6].

A: Given : The function is f(x) = 6x + 4 +24x and the closed interval [ 1, 6 ].

Q: 66. What will be the function g(x) resulting from normalizing the function f(x) = x³ − x4 defined in…

A: To find : function gx resulting from normalizing the function fx=x3-x4 defined in the domain 0, 34

Q: 95. Prove that the average rate of change of the linear function f(x) = −2x + 4 on any interval I is…

A: The average rate of change of a function f(x) over an interval [a,b] is given by f(b)-f(a)b-a. It is…

Q: Use the e - S definition to show that the function x- 1 f(x) = x +2 %3D is continuous at x = 3.

A:

Q: Use the Max-Min Inequality to find upper and lower bounds for the value of dx. 1 + x

A:

Q: What is the domain of ln |x| ?

A: Given: fx=lnx To determine: Domain of a given function.

Q: Use the mean-value Theorem to prove 1 1 - < ln(x + 1) − ln x < - X x +1

A: Consider the function f(x)=ln(x) So, f(x) is continuous on 0,∞ and f(x) is differentiable on 0,∞.…

Q: For function, find (a) the critical numbers; (b) the open intervals where the function is…

A: Consider the function, y=x-4ln3x-9 Differentiate the given function with respect to “x” then,…

Q: write cosh(4 ln x) as a rational function of x

A: To solve the given problem apply the following formula

Q: How must f(0) be determined so that the function f(x) = x2-x ニー x0, is continuous x-1 at X= 0?

A: Let f be a real function . Let a be any point in its domain . If limx→afx exist and equal to fa Then…

Q: In the function:  f(x)= (3x^2)ln(x) , x&gt;0 When is the function concave up and concave down in…

A: For concavity we need second derivative.

Q: The function h(x)=In(x² +c) is concave up on the interval (-4,4) and concave down on the intervals…

A:

Q: find f'(x) for f(x) = 2xtan-1 x - ln(1+x2)

A:

Q: Find the absolute extrema of f(x) = −x^(2) + 3x on the interval [0,3] .

A:

Q: Use the Intermediate Value Theorem to show that 2x – 3 - if – 3 0 has a zero on the interval [-2,…

A: First compute the function if they are continuous then apply the intermediate value theorem.

Q: Consider the function f(x) = x – 3 ln(x) on the interval 3 The absolute maximum value is and this…

A:

Q: Find the absolute maximum and absolute minimum values of f on the given interval. ln(x^2+3x+8) in…

A: Given:

Q: What is the domain of g(x)=ln(25x-x^2) Show all the work.

A:

Q: In the function:  f(x)= (3x^2)ln(x) , x&gt;0 Where is the function increasing and decreasing in…

A:

Q: Find the absolute extrema of f (x) = x-12x on the closed interval [0, 4].

A: The given function is, fx=x3-12x The interval is 0, 4

Q: Estimate the value of df/dx for f(x) = root 8x at x = 3, using any method

A: To find the derivative of f(X), differentiate with respect to X on each side.

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x2 -…

A:

Q: the net signed area between the curve of the function f(x) = 2x and the x-axis over the interval…

A:

Q: Let f(x)=1x−2 ; for what values of x , f(x) will be discontinuous?

A:

Q: Consider the function f(x) = x - 3 ln(x) on the interval The absolute maximum value is and this…

A: Consider the given function, fx=x-3lnx differentiate the function with respect to x,…

Q: Determine the interval(s) on which f(x)=square root(x/x-4) is continuous.

A: Given query is to find the interval where function is continuous.

Q: Prove that f(x) = x-¹/2 is: (i) not sectionally continuous in every finite interval in the range x ≥…

A:

Q: 4. Find the absolute extrema (abs. max and min) of f (x) = x2 - 8x - 1 on the interval [1, 10].

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.