f(x) 0 for all x in the open interval (10, 14).

Q: Ax, y) = In(x +y)

A: In this question, we have to find the domain and range of f(x,y)=lnx+y As we know that the domain of…

Q: The function f(x) =3 x4-4 x3-12 x2+1, is increasing on the interval

A: f(x) = 3x4-4x3-12x2+1f'(x) = 12x3-12x2-24xf'(x) = 12x(x2-x-2)f'(x) = 12x(x2-2x+x-2)f'(x) =…

Q: Find the absolute extrema of the function f (x) = 30x – x² over the interval (-o, 00)

A:

Q: Find the absolute extrema of the function on the closed interval.                         f(x) = 2x3…

A: We find the critical points by solving f'(x)=0 -1 is not in the interval [0,3] 1 lies in [0,3]

Q: Find the funchion f Such that F(x) xf (x)-x and fo) 2

A: Convert the given problem to a simple differential equation and solve the same.

Q: Find all relative extrema in the function k(x) = (x2 – 4)-2 on the interval [-3, 3].

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 constant a such that the function sin x -13 - S(x) = %3D a+ 11x, x 20 is continuous on the…

A:

Q: Consider the function f(x)=5x+6x^2 over the interval [0,1].

A: Given that :-         f(x) = 5x+6x2 over [0,1] (a)  By deviding the interval into n sub intervals of…

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

A: The given function is Solve the absolute extrema on closed interval [0,4] by finding its derivative…

Q: For the function f(x) = -2x + 3x2 + 12x 1. Find all the critical points of the function f(x). 2.…

A:

Q: 3 Determine the intervals for which the function f(x) = x° + 18x +2, is decreasing.

A:

Q: Find the absolute extrema of f(x) = x³ - 6x - 1 on the interval [-2,3].

A:

Q: 9. Use the Intermediate value theorem to show that f(x) = 2x( – 3 has a zero in the interval [1,2].

A:

Q: x- 1 f(x) = x + 2 %3D is continuous at x = 3.

A: Check function is continuous or not at x=3

Q: Find the absolute extrema of the function f(x)= (x+2)4 (x2 -8)2  on the interval [-4,1].

A: Given,f(x)=x+22x2-82 An absolute extremum of a function in a given interval is the point at which a…

Q: Prove that f(x) = x 2 takes on the value 0.5 in the interval [0, 1].

A: We have to prove that f(x)=x2 takes on the value 0.5 in the interval [0, 1].

Q: Approximate f(3) centered at 0 of f(x) = 2x³ + 3x² + x - 1. %3D

A:

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

A: The critical points of the function are the points where the function is defined but its first…

Q: (B) The function f(x) = x² + x +1 has no fixed point, prove that.

A: Let X be a nonempty set and f : X → X. A point x ∈ X is a fixed point of  f, if f(x) =x.  If no…

Q: Find the absolute extrema of the function on the closed interval.

A: Relative extremum of a function are critical points of the function. Critical points of a function…

Q: How many functions f:R→R  exists such that : 2f(x)+2f(y)=f(x+y)+f(x−y)+2y holds for all real x and…

A: By choosing x=y=0. Also by choosing x=y we can see f(2x)=4f(x).  Moreover choose x=0 and use f(0)=0,…

Q: Find the interval in which the function is positive. f(x) = x2 - 7x + 10 %3D I. (- , 2) II. (2, 5)…

A:

Q: For f(z) = 2z', find ip using the definition,

A: The limit definition of a derivative of a function, f(x) at a point, x=a is given by .

Q: The interval over which the function f(x) = becomes continuous is %3D x+8 (-3, 0) (-3, 3) (-00,…

A:

Q: Find the absolute extrema of the function on the closed interval.                        f(x) = 7x2…

A:

Q: Find the values of a and b that make f(x) continuous for all real numbers. (x+2, f(x) = { ax³, (x² +…

A: Given that f is a continuous function, then it is continuous at all the point. So, the function is…

Q: Determine f such that f′′(x) = 12x − 1 and 1 is both a critical number and a y- intercept of f

A: Given:  and 1 is both critical number and y-intercept.

Q: Prove that f (x) = x2 takes on the value 0.5 in the interval [0, 1].

A: Here given

Q: The function f(x)=/25-x' is contionous on

A: It is continuous function.

Q: The function f(x) = 2x° – 36x2 + 162x – 11 has two critical numbers. The smaller one equals and The…

A:

Q: Find the absolute extrema of the function ƒ(x) = 3x2/3 - 3x5/3 on the interval [0, 8].

A: Given ƒx = 3x2/3 − 3x5/3 on the interval 0, 8.

Q: Find the absolute extrema of the function on the closed interval.                    f(x) = x2 + 5x,…

A: Absolute extrema of the function on the closed interval occurs at a point where its first derivative…

Q: On which interval is f(x) = x³ – 12x + 12 decreasing? ㅇ (-8;2) ㅇ (-8, +8) | O (-2,+0) O (-2, 2) O…

A:

Q: The function f(x) = 2x 33x + 168r - 1 has two critical numbers. - The smaller one is x = and the…

A: In this question we are given with function x and we have to find the critical points of the…

Q: Find the values of a and b that make f(x) continuous for all real numbers. (x+ 2, f(x) = { ax³, (x²…

A: f(x)=x+2,x≤-1ax3,-1<x≤1x2+bx,x>1

Q: find the absolute extrema of f(x)= 4x^2-48ln(x) on the interval [.4, 5]

A: Given function is  f(x)=4x2-48ln(x) Differentiate both sides with respect to x. f'(x)=8x-48x Now,…

Q: Show that the function f(x) = 1 – I - x² is continuous on the interval [-1, 1].

A:

Q: The function f(x) = 2 + 3x² – x³ is concave upward on the interval: (-∞, 1) (1, ∞0) (-∞, 0∞0) None

A:

Q: Find the critical numbers of the function. f(x) = x8In(x) %3D X =

A: Consider the function  f(x)=x−8lnx

Q: Find all the x-intercepts of f(x)=cos(x) on the interval [0,2π)

A:

Q: Find the constant a such that the function is continuous on the entire real line. (9x², Flx) = {9x?,…

A: Given function is : fx=9x2    ,      x≥1ax-6   ,    x<1 Here given that function is continuous…

Q: Find the interval(s) on which f(x) = 2x^3-3x^2-12x+1 is concave up.

A: Given : fx = 2x3 - 3x2 - 12x + 1

Q: between the graph of f(x) = x²- 2x and the x axis over the indicated interval [1, 2]

A:

Q: Consider the function f(x) = 12x + 45x4 – 200x³ + 5. For this - function there are four important…

A: The given function is: fx=12x5+45x4-200x3+5 To find the critical points of this function, first,…

Q: The function f(x) = -x* + 6x + 2 is concave %3D up on: Select one: O (-00, -V3) and (V3, 0) O (-1,…

A: The given function is f(x)=-x4+6x2+2

Q: Verify Rolle's theorem for f(x) = x² - 9x +6 over the interval [0, 3].

A:

Q: The function f(x) = x³ – 3x² + 5 is concave upward on the interval O (-∞, 1) (1, co) (-∞0, ∞0) O…

A: