Evaluate the function for the given values of x. 5) -5x + 4, for x<-1 x< + 3, for -1 s x<2 1, for x > 2 f(x) = %3D (a) f(-1); (b) f(3) `

Q: Use the table below to compute h'(-1) for h(x) = f(x) g(). (E) (), (1)6 () 1/2 -2 2 1 -3 1 2 1 4. -1…

A:

Q: 1. Find the local extrema of f(x) = x* – 2r2 +1, and state the intervals on which this function is…

A:

Q: Which of the following is the appropriate function used in finding the value of. V2-1 f(x) =x² -…

A: f(x) =x^2 - 2x-1

Q: 2. Find the absolute maximum and absolute minimum of the following function on the given interval.…

A:

Q: 2. Find the value of k so that the function Sa² + 25 |kæ – 40 is continuous at x = 5. defined by…

A: Given,          The function defined by fx=x2+25    x≤5kx-40    x&gt;5           is continuous at…

Q: Find (f/g) (n) when f(n) = x^2 - 3x - 4 and g(n) = x + 1 _____________________ A. x + 2 B. x - 1 C.…

A:

Q: 3) Given the function f(x)=x² - 5x+3 on the interval [0,4] find the value c guaranteed by the Mean…

A: The given function is continuous on the interval [0,4], to find the value of  c, Apply the mean…

Q: Evaluate the function for the given values of x. -Зх+7 for x<-1 f (x) = *+2 for - 1<x<5 6. for x25…

A: Given query is to find the value fo the function at indicated points.

Q: Based on the graphs of f(x) and g(x), in which interval(s) are both functions increasing?…

A: Domain of g(x) can be broken into following intervals: (-inf,-3), (-3,-1) and (-1,inf) In each…

Q: 5. The function f(x) is defined as: 4x3 +17x2 + 13x +36 x -4 ontinuous for all values of x. What…

A: solution:-f(x)=4x3+17x2+13x+36x+4     x&lt;-45x2+2x+a                       x≥-4f(x) is continuous…

Q: Find the value of k so that the function ( 5x +3 if x<3 f(x) = | kx² is continuous everywhere? if x…

A:

Q: Let h(x) = f(x)g(x). If f(x) = -x - 4 and g(x) = In(2x2 – 2x – 4), what is h'(x)? %3D Select the…

A:

Q: 4. Given the function f(x) = x3 In x. Determine the following: a. Domain b. X intercept(s)

A:

Q: Consider the following piecewise function where c is a constant real number. Зx2 + 5с х 2 3x2 + 5c x…

A: For limit to be existing both left side limit and right side limit should be equal

Q: (a) Let f(x) = x³ +x² + kx, k a constant. For what val- ues of k is f one-to-one? (b) Let g(x) = x³…

A:

Q: The graph of the function f(x) = -x³ + 18.x² – 8 is concave upward on o (3,5) None of these o (3,7)…

A:

Q: 4. Given the function f(x) = x³In x. Determine the following: %3D g. Intervals where the function is…

A:

Q: D) Identify the even function among the following. A) f(x) = 2|x| - x² %3D B) h (x) = 2x – x² %3D C)…

A:

Q: 3. Find the absolute extrema of the following function on the indicated interval. f(x) = x3 + 2x² –…

A:

Q: The critical number(s), if any, of the function f(x) = (x²-3x+2) is (are):

A: critical points of fx=x2-3x+2-13

Q: 2. Let f(x) = e" + for x E [0,3]. Determine the length of the graph of f. 4e

A:

Q: 1. Find the value of c to make the following piecewise function continuous on the the interval (-o,…

A:

Q: 1 Given f(x) =x2- 1, find the value f(p). p² + 1 p² - 1 p² - 2p + 1

A:

Q: 3. Given f(x)=-x+4x+12, 0sx58: (a) Carefully, graph S(x), 0Sx s8.

A:

Q: 12. Find the value of k that will ensure that the following function is continuous at x = 3: x² + k…

A: As we know that the function is continuous at x=a if:   limx→a-f(x)=limx→a+f(x)=finite…

Q: (b) Suppose f'(x) > 1 for all x > 0, and f(0) = 0. Show that f(x) > x for all x> 0.

A: We will be using mean value theorem

Q: If f) (E-1) and g(x) = (-1) then the function () (x) is (2z-5) %3D (2x+5) (2x-5) (2x+5) (x-1) (x-1)…

A:

Q: 1. Use the definition to find f'(e) if it exists *, if z< 3 S(x) = c= 3 -3r, if r 23

A:

Q: If we apply Rolle's Theorem to the function f(x) = 2x² – 12x - 7 on the interval (1, 5, how many…

A:

Q: The equation for a family of functions with zeros at +3, and -1, with end behaviors from Q2→Q4 is:…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Find the length L of the graph of 3 (a) f(x)=x'2 +1 for 0<x< 4 3/2 1 (b) f(x)=In x -x² for 1<x<2 8

A:

Q: If we apply Rolle's Theorem to the function f(x) = 2x- 16x 6 on the interval [2, 6|, how many values…

A:

Q: What are all values of x for which the function f defined by f (x) = a+3z2 - 9x +7 is increasing?…

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: Let f(x) (x- 2)3. a. Does f'(2) exist? b. Show that the only local extreme value of f occurs at x 2…

A:

Q: Find the range of f(x)=x-5x+6. O (-00, 1/4] O -1/4, co) O (-00, 00)

A: Range of Quadratic Functions Graphically : The range of a function y = f(x) is the set of values y…

Q: The critical points of the function f(x) = 16x? 2x4 occur at O r = 0, x = ±2.67 O x = 0, x = ±1.00 O…

A:

Q: 5) Given f(x) = V1 -x² , the range is: a) O (-∞; -1] b) O [-1, 1] c) O All real numbers d) O [[0,…

A: The graph is shown below:

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: Evaluate the function for the given values of x. -3x+6 for x<-1 f(x) = x²+2 for -1<x<4 for x24 Part…

A:

Q: 7. For the function f (x) = In(x² + 1) (a) find all intervals where f is increasing, (b) find all…

A:

Q: The critical points of the function f(x) = 9x? – 2x4 occur at, x = 0, x = 1.20 %3D x = 0, x = ±1.50…

A:

Q: 2. Find the value of k so that the function defined ( x2 + 4 x 2 - x = 2.

A: A function is a relation which maps each value in its domain to exactly one value in its range.…

Q: If we apply Rolle's Theorem to the function f(x) = 2x² - 8x - 1 on the interval [0, 4], how many…

A:

Q: For what value (s) of x is the function f(x)  -4 if  x ≤ -5…

A:

Q: If we apply Rolle's Theorem to the function f(x) = 2x² – 20x – 9 on the interval [3, 7], how many…

A:

Q: Given the function x2 - 4 x<2 X- 2 f(x) =. ax3 – bx +3; 2sx<3 2x- a + b; X23 the values of a and b…

A: It seems that the given options are not correct at all   We will find the correct options using…

Q: f(x) = v x² + 5x - X

A:

Q: Show that the following functions has a solution on the indicated intervals f(x)=x³ + 2x = x² + 1…

A: solution:- f(x)=x³+ 2x =x² + 1,      x∈ (0,1)f(x)=x³+ 2x -x² - 1=0Intermediate value theoremf(x) is…