Let the function ƒ be defined by -5x + 4 for æ < -1 for -1 2 f (x) = { z +3 %3D 1 Evaluate f(-1) + f(3)

Q: B) Test the functions continuity at the given poihts: (x²-x-6 1) f(x) 3D x * 3 ,at x 3, x 5 X-3 x =…

A: f(x)=x2-x-6x-3x≠35x=3

Q: Prove algebraic ally that any function of the form f(x)=ax2n+4 (where n is an integer) is symmetric…

A: The given function is fx=ax2x+4. To prove fx=ax2x+4 is symmetric to the y-axis, it is enough to…

Q: Let f (x) = x3 - 7x. %3D Find all numbers c in the interval (-2, 0) for which the line tangent to…

A: given function is                                                  f(x)=x3-7x interval is    c∈(-2,…

Q: Prove that the function given by f(x) =x3-3x2+3x-100 is increasing in R

A:

Q: Let ø : R³ → R be a C² function that is zero for all x € R³ with |x| > R for some big R. Then show…

A: As per the question we have to derive a defination of the Dirac-Delta function. And then using it's…

Q: Suppose f'(x) = x² - 1. Then the graph of f is concave upward on 0 (-∞0,0) O (-1,1) (0,00) O (-∞,…

A:

Q: Find the absolute maximum and minimum values of f on the given closed interval, and state where…

A: We first have to find the critical points. For that we find f'(x). Then set f'(x)=0 and solve for x.…

Q: Prove that f(x) = (x – 1)2 + (x + 1)? is an even function. A function k(x) is an even function if…

A:

Q: constant k is the functionf defined by if x +0 f(x) = V5- x - V5+x k if x = 0 continuous at x = 0?…

A: On putting limit x tends to 0 when condition of not equality it becomes 0/0 form . So by…

Q: Find the values of k for which the function f is continuous everywhere. k +2 if x< 1 f(x) if x2 1

A: the given function is a piecewise polynomial function therefore it is continuous at every point and…

Q: (a)Verify Rolle's Theorem for f (x)=x - 16x+10 over the interval [0,4].

A:

Q: snip

A: A function f is decreasing on an open interval I, if for any choice of x1 and x2 in I, with…

Q: Let f(x) = (|x| + x2 − 1     if x ≤ 0          (|x| − x2 − 1     if x > 0 Is there some x in (−1, 1)…

A:

Q: 2, if x 0 Evaluate the piecewise function at the indicated values from the domain: f(x) = at x=-8…

A:

Q: all values of k that would make the function f (x) continuous at x = 3. I values of k exist, submit…

A:

Q: What are the local extreme values of the function f(x) = x' – 3x + 2? a. None of these. O b. Local…

A:

Q: Find the absolute maximum and absolute minimum values of f on the.given interval. (4) f(x)= -3,31…

A:

Q: Let f: R R and let f(x) >0 for all xER. Show that f(x) is strictly increasing if and only if the…

A:

Q: If f(x)=3*-9 and g(x)= tanx, then what is the domain of (g+f)(x) on the interval [0,2m]?

A:

Q: Find the value of that will make the function f(x) continuous everywhere. f(x) = {ka² -2, (4x+k,…

A: Given function is- f(x)=4x+kx≤-5kx2-2x&gt;-5 To find- To find the value of k that will make the…

Q: Does there exist a function f such that f(0)  =-1, f(2)  =4, and f'(x) ≤ 2  for all  x?

A:

Q: Select the graph of a function f that satisfies f' 0 on (-0, -1)U(-1, 0).

A: means f is decreasing for x&gt; - 1   means f(x) is concave up on both sides of x=-1

Q: Let f(x) = Vx +7 and g(x) = x +3 a) Find (2) (2) show work. b) Give the domain of the function (-)…

A:

Q: The function is said to be in this value if f(xo) 2f(x) for all x in an open interval. O Relative…

A: Given that: f(x0)≥f(x)

Q: Let f(x)=x^3−9x. Using Rolle's Theorem, what are all the values c in the interval [-3, 3] such that…

A:

Q: For the function f(x) = Ax2 + Bx + C, determine the value of c guaranteed by the Mean Value Theorem…

A: f(x) = Ax2 + Bx + C f'(x)=2Ax+B By Mean value theorem:

Q: let f: R^ -> R be a function given by 2 f(x₁, x₂... x₁) x.x²2. x²n, where = € 2.1 Show that the…

A:

Q: 7. Find the value of K that makes the function f(x) = (x² + 2 , x > 5 (x² – xk – 3 , x< 5 Continuous…

A:

Q: Verify the mean value theorem for the function f(x)= x(x²-x-2) over the interval [-1.1)

A:

Q: Let f be the function (8x-1 for x х Find the values of a and b that make the function continuous.

A:

Q: (2) of the function f(x) such that F(1) = 4. Preview

A:

Q: Find x for which f(x) is not continuous: 3 x-1 f(x) =-+ x'x2 -1

A:

Q: 3. Determine the values of a and b if the given function f(x) is continuous. 1 ,x 2

A:

Q: 14. Determine if the function f(x)=2x°V4-x* is either even, odd, or neither (even nor odd). Does the…

A:

Q: Find the value of k so that the function f is k-x2 x3 X< 3 continuous at x=3 and f(x) х-8

A: Given, fx = k-x2x≤3x-8x&gt;3   We have to find the value of k so that function is continuous at x =…

Q: Let f be the function defined by f (x) = 6x. On which open intervals is ƒ decreasing? %3D -2 3 <글…

A: Given that: f(x)=x33-x22-6x

Q: Let f be a real-valued function on R. Suppose that f(−1) = 3 and f'(x) ≤ 2 for all values of x. How…

A: f(-1)=3f'(x)≤2Integrating w.r.t x;∫ f'(x) dx ≤ ∫2 dxf(x)≤2x+Cf(-1)=33=2(-1)+CC=3+2C=5

Q: 2. Define a function 6x2-x-15 3x-5 f(x) = |k, 3 (a) Find a value of k so that f(x) is a continuous…

A:

Q: The piecewise function f(x) is defined below. f(x) = {kx² - 4, Is-2 x+ 2, xS-2 x>-2 For what value…

A:

Q: True or False A function f is decreasing on an interval I if, for any choice of x1 and x2 in I, with…

A: Given: True or False A function f is decreasing on an interval I if, for any choice of x1 and x2 in…

Q: If the graph of a function f(x) is decreasing over the interval (a, b) then which of the following…

A:

Q: Find the discontinuities of the function 2х — 1 - if 2 < x x +1 1 Let G be the function defined by…

A: Given,

Q: Let f(x)=x² defined a function on the closed interval −2 ≤ x ≤ 8. 1. f (4) 2. f(-3) 3. f (t – 3)

A:

Q: If f is differentiable and f'(x)=x³-2x²-x+2, then fis increasing or

A: Given, x³−2x²−x+2=f' We equate the given function to zero for critical points. x³−2x²−x+2=0   Step…

Q: 1 Let f(x) Find f'(x). 3 (z4 – )* - f'(x) =]

A:

Q: D. Discuss the continuity of the function on the closed interval. Function Interval 1. g(x) V49 [-7,…

A: Note: We are entitled to solve only one question at a time. Given: gx=49-x2 To Discuss: Continuity…

Q: Let g(x)=V 64x2 - 4 The function g is increasing on the following interval(s): O (-∞, 0)

A: Solution: The objective is to determine the intervals where the given function is decreasing and…

Q: Find the absolute extrema of the function on the closed interval.                   f(x) = 4x / (x2…

A: f(x)= 4xx2+9so,  f1(x)= 4(x2+9) - 4x(2x)(x2+9)2Now equ    f1(x)=0=                4(x2+9) -4 x(2x) =…