ove that the function given by f(x) =x³-3x-+3x-I00 is increasing in R

Q: (c) For what values of a and b does the function (ах- 3, x< 4 f(x) = } (-x? + 10x - b, x24 satisfies…

A:

Q: O Find the intervals where f (x)= x -x* is increasing/ decreasing and concave up /down.

A:

Q: 3) Verify Rolle's Theorem for the function f(x) = 4x² + 6 defined over the interval [-5, 5]. Justify…

A: Rolle’s Theorem has 4 conditions to be proved.

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

A: Given: To Find: Absolute extrema of the function on the closed interval. Concept:

Q: True or False The graph of the function f(x) = x is increasing on the interval (0, 0). (pp. 69-77)

A: Given :             The function f(x) = x2.

Q: Determine if the function f(x) is continuous and/or differentiable at x = 1? x +5 for - 1sxS1 f(x) =…

A: The given function is f(x)=x+5    for -1≤x≤16x       for  1&gt;x≤4 The function is said to be…

Q: 3)Verify Rolle's Theorem for the function f(x) = 2x2 + 4 defined over the interval [-6, 6]. Justify…

A: Rolle's theorem is satisfied if : f(x) is continous at given interval. f(x) is differentiable at…

Q: a)= 3ス2-3 %3D

A:

Q: Find the values of x for which the function is continuous. (Enter your answer using interval…

A: The function is given as fx=4-x      if x&lt;3 2x-5    if x≥3 find values of x for which the…

Q: 3)Verify Rolle's Theorem for the function f(x) = 5x2 + 6 defined over the interval [-3, 3]. Justify…

A:

Q: Determine the absolute extrema of the function f(x) = (x-3)ex on the interval -1≤ x ≤ 3.

A:

Q: Determine where the function f(x) is continuous. f(x) = Vx2 - 100 The function is continuous on the…

A: Under the square root, we can not have a negative number.  x2-100≥0x2≥100x≥10 or x≤-10 In those…

Q: 3)Verify Rolle's Theorem for the function f (x) = 4x² + 7 defined over the interval |-6, 6|. Justify…

A: Rolle's theorem:- If a function f is continuous on Close interval [a,b] and differentiable on open…

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: b) State what it means for a function to be continuous at a point x = a.

A:

Q: Find the interval(s) where the function is increasing and interval(s) where its decreasing. 1- x2 2.…

A: We need to find the intervals in which the given function is increasing and decreasing.

Q: 3) Verify Rolle's Theorem for the function f(x) = 4x2 + 4 defined over the interval -3, 3. Justify…

A: Solve the following

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

A: Given function is, fx=6−x,   −4,1 To find the absolute extrema of the function on the closed…

Q: Find the absolute extreme values of the function on the interval f(x)=tanx, -pie/6 less than or…

A: To find the extreme values of the function on the interval, f(x)=tanx, -π6≤x≤π6

Q: Determine the absolute extrema of the function f(x) (x- 4)e on the interval-1 <x<4. SHOW YOUR WORK!

A: We have given f(x) = (x – 4)ex on the interval -1 ≤ x ≤ 4.

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

A: Given function:

Q: uppose f(x) = 4nxe for all x E R. Show that f = -f. -e

A:

Q: 'B4(a): Verify Mean value theorem for the function f(x) = 6x³ + x + 4 over the interval [0, 1].

A:

Q: 2. Determine the interval(s) where F(x) is increasing. Justify your answer.

A: 2.According to the graph of function f(x ) is defined as   f(x)=x+2     -5≤x≤-24-x2   -2≤x≤232x-3…

Q: Find the absolute extrema of the function on the closed interval.                         f (x) = 3…

A: Given equation is   f(x) = 3-x The absolute maxima or minima occur either on the critical points or…

Q: 81. f(x) = |x – 5|

A:

Q: The absolute Extrema of the function f(x) = –x^2/3onthe interval (-8, 0 )are

A: To Determine: The absolute Extrema of the function on the interval (-8, 0 ) are…

Q: Locate the absolute extrema of the function on the closed interval. f(t) = ₂, [3,5]

A:

Q: ): Verify Mean value theorem for the function f(x) = 3x° + x + 4 over the interval (0, 1].

A:

Q: 3)Verify Rolle's Theorem for the function f(x) = 2x² + 6 defined over the interval [-4, 4]. Justify…

A: The function is f(x)=2x2+6   Rolle's Theorem: If f(x) is continuous on the interval [a, b] and…

Q: Q2: (20 mark) a) Differentiate the function f(x) = tanx -1 secx

A: We can solve this problem using quatiant rule of derivative.

Q: over what domain interval is f(x)=|x| increasing?

A: Consider the given function fx=x

Q: Sx? -1, x <3 f(x) = Continuous at x-3 ? (2ax , x 23

A:

Q: III. Show that the function is continuous on the specified interval. 11. f (x) = V3x – 5; [3,9]

A:

Q: ] B4(a): Verify Mean value theorem for the function f(x) = 3x³3+x + 2 over the interval (0, 1].

A: Use Lagrange mean value theorem

Q: Find the largest open interval where the function is changing as requested. 1 Increasing f(x) =2.1 O…

A:

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

A:

Q: 5. Use calculus to find the interval(s) on which the function f(x) = x-e increases.

A:

Q: Determine where the function f(x) is continuous. f(x) = Vx-1 The function is continuous on the…

A: If f(x) is defined then it is continuous

Q: - Is the function given by f(x): X the interval (-7, 7)? Why or why not? +3 continuous over

A: Topic:- function

Q: B4(a): Verify Mean value theorem for the function f(x) = 5x³ + x + 5 over the interval [0, 1].

A:

Q: Find the constant a such that the function is continuous on the entire real number line. Sx³, x 2…

A: Given : f(x) = x3,x≤2ax2,x&gt;2 and the function is continuous. To find : value of a?

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: On which interval is f(x) = x – 12x + 12 decreasing? o (-2, 2) o (-00, 2) o (-0, -2) U (2, +0) ㅇ…

A: Let's find.

Q: Find the number c that satisfes the conclusion of the Mean Value Theorem on the function f(x) = x³…

A: Given f(x)=x^3 on [0,4] Here we have to apply the Lagrange's mean value theorem to find the c value.

Q: 1 3 In y = In (5x + 7) - - In (x + 9) + In C 3

A: The equation is given by 3ln(y) = 12ln(5x+7)-13ln(x+9)+ln(C) To determine : The expression for y as…

Q: 3) Verify Rolle's Theorem for the function f(x) = 4x2 + 6 defined over the interval [-3, 3]. Justify…

A:

Q: (c) For what values of a and b does the function (ах- 3, x< 4 f(x) = -x² + 10x - b, x2 4 satisfies…

A: