19. Find the value of a that makes the following function differentiable for all values of x. if x<0 ax g(x)= . x2 – 11x if x20 The function g(x) is differentiable for all values of x when a= (Simplify your answer.)

Q: b)f(x) = Vx²

A:

Q: 4) Find the value of the function f (x) given in the table below at the point x = 3 by Aitken…

A: to find the value of fx given in the table at the point x=3 by Aitken method  solution we will solve…

Q: b) Suppose that f(x) = }Bx + 2 SBx² – 3 if x 2 Find the value of ß so that f(x) is continuous…

A: The given continuous function is,

Q: For what value of the constant c is the function f continuous on (-∞, ∞)? ( cx2 + 2x x3 - cx if x <…

A: We know that for any value of c, for x &lt; 5, the function is continuous and for x &gt;= 5, the…

Q: 2. Evaluate the piecewise function at the given values of the independent variable. 4x +4 if x < 0…

A:

Q: 1) Find all relative extrema in the function f (x) = x 3 + 3x2 – 24x + 12.

A: For relative extrema the derivative of the function will be zero. Thus,…

Q: 1.4 For which values of a ER is the function f(x+ iy) = (a²x – axy) + i ax? + ay an entire function?

A:

Q: 1) Find all relative extrema in the function f (x) = x³ + 3x2 – 24x + 12. 2) Find all points of…

A:

Q: Answer the following questions for the function f(x) = xVx + 4 defined on the interval – 6 < x < 4.…

A: Given fx=xx2+4-6≤x≤4

Q: 4. State all the values of x in which f(x) is not differentiable. Justify your answer. b) f(x) = - 2…

A: Given: 4. State all values of x in which f(x) is not differentiable.(a) From the graph given above…

Q: 2. Consider the following function: y = f(x) = x" – 14x® (a) Determine in which regions this…

A: A function is increasing or decreasing that is determine by    f'(x)&gt;0 or f'(x)&lt;0 A function…

Q: 2. Evaluate whether the following initial values is true in the function: y = 4cos-+ e-2x 2.a) 2.b)…

A: Given , y=4 cosx2+e-2x

Q: Answer the following questions for the function f(x) = xVx+ 25 defined on the interval -7 < a < 5.…

A: Given that the function is        f(x) = x√(x2+25)    , -7&lt;=x&lt;=5 .

Q: (i) Discuss the continuity of the function f(x) = {x2²− 3x        if x &lt; 2           2x + 4…

A: We are entitled to solve one question at a time, so I am providing solution for first question.…

Q: (i) Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 2 2x + 4 if x ≥ 2on the open…

A:

Q: 3.4 Differentiate f(x) = a°x* - 5ax with respect to x. Assume that a is a constant. f'(x) =D

A:

Q: 17. Given the function f (x) = x2 + 2. Find and simplify the difference quotient. S(x+h)-f(x) h 0

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: b. For what value of (k) is the function y=f(x) continuous at x=3. x3-3x2-4x+12 x#3 x-3 f(x) = k x =…

A:

Q: 2. Consider the following function: y = f(x) = x" – 14° (a) Determine in which regions this function…

A:

Q: 3. Consider the following functions: f(z)) = x² + 16 9(=)) = (x – 16)² h((x)) = (x + 1)² – 16…

A: Given: f(x)=x2+16g(x)=(x-16)2 and h(x)=(x+1)2-16

Q: 1. Find the value of a that makes the following function differen- tiable for all x-values. Jax, if…

A: gx=ax,if x&lt;0x2-3x,if x≥0

Q: For what value of c is the function f(x) = = C= C 7 2-4 (x+2)(x-3) x==2 x = 1 otherwise continuous…

A: Given :fx=c,      x=-27,        x=1x2-4x+2x-3   otherwise

Q: 2. Find the x-coordinate of the point(s) of discontinuity of the following functions -16 x3 16х — 4,…

A: For x&lt; 3 , f(x)= -16 is continuousFor 3&lt;x&lt;6 , f(x)=16x-4 is continuous tooFor x&gt;6 ,…

Q: For what value of the constant c is the .! function f continuous at x-3 |cx – 2 , if x 3 2 -1 -2 1

A: If function is continous then,limx→n+ fx =limx→n  fx = fnat point nso at given point x=3limx→3+ fx…

Q: 1. Use the function f(x) = 4x°e* to answer the following problems: (a) On which interval(s) is the…

A: The given function is: fx=4x3 ex (a) To find the interval in which the function f(x) increasing?

Q: Find the value for k so that the function will be continuous at x = -1. S 9x - 18 l-x² - 4x – 4 + k…

A:

Q: 3. Suppose that for a company producing r face shields per week, the cost (C) and revenue (R)…

A:

Q: For what value of the constant c is the function f continuous on (-o S cx2 + 8x x3 – cx if x 3 с 3

A:

Q: 14. If f(x)= x+4 and h(x)= 4x-1, find function g(x) such that gof =h. %3D

A: Given that , fx=x+4 and nx=4x-1We have to find gx such that got=h

Q: 5. Find the x-coordinates for all points of discontinuity for f(x)- 「X316, xśl x〉 1 2 c. 1, 32d.…

A: First we check the limits as x approaches to 1 from left side and right side .

Q: 8. Analyze the differentiability of the following function: f(t) = Vx² – 2 State the restrictions in…

A:

Q: 12. If f(x) is a non-constant linear fucntion and g(x) is a quadratic function, then what type of…

A: f(x) is linear function so f(x) can be expressed as  f(x)=ax+b, where a≠0 and b are constants. g(x)…

Q: 2. Determine the given function is continuous or discontinuous at t =-2 (t² + 2 6. t -2

A: Given information : t=-2

Q: if x 2 1. Determine the constant k such that the function f(x) = is continuous at x = 2.

A: As per guidelines, I can answer maximum one question. Since you have asked for multiple questions,…

Q: (b) For what values of the constants c and d is the function continuous and differentiable for all…

A:

Q: 2 The linear approximation for the function f(x) = be used to estimate f(0.01). Which of the…

A:

Q: Answer the following questions for the function f(x) = x/x² +1 defined on the interval – 6 < x < 4.…

A: We have to find intervals for concave up and concave down, inflection point and minimum, maximum.

Q: Given the function y=f(x), y' is found to be negative over the interval (4,8), then over this…

A: Given:→y=fx→y'&lt;0 for 4,8Then to find the nature of fx

Q: Do you agree with the contention that the functions f(x) = x + 2 and g(x) = x2 − 4/x − 2 are the…

A: I am not agreed with this fact that f(x) and  g(x) are the same in every respect. The reason behind…

Q: 1/ Find the domain of the following functions : 1 1) f(x, y) = x²+y²+z²+16 2) f(x,y) = In(9 - x² –…

A:

Q: 10 Q4 For the functions f(x) = 7x + 4, h(x) =-3 and g(x) = 3x-2 (a) Evaluate (1) g(4) (ii) h{g(4)}…

A: It is given that fx=7x+4,  hx=10x-3,  and  gx=3x-2. (a) Evaluate: (i) Find the value of g4.…

Q: 2. Find the value of k so that the function defined by f(x) Sx² + 20 x 5 continuous at x = = 5.

A: We know that, a function fx is said to be continuous at x=a if and only if Left hand limit=Value of…

Q: For what value of c is the function below continuous at x=-3? f(x) = { c  when x=-3 1 when x = 1…

A: The function                     f(x)=c                       when x=-31                       when…

Q: 9 Check if the following function increase or decrease at given points. x²+4 f (x) = xo = 0, x¡ = 3…

A:

Q: 38. At what value of x should the function f(x) = In(x – 4) approach to so that f(x) will be as…

A:

Q: (Bx2 – 3 Bx +2 if Suppose that f(x) = x< 2 if Find the value of ß so that f(x) is continuous…

A:

Q: 3. Do you agree with the contention that the functions f(x) = x+2 and g(x) x-2 are the same in every…

A:

Q: 2. Determine the given function is continuous or discontinuous at t=-2 (t² + 2 t -2 If f(t) = {6 t…

A:

Q: For what value of the constant b is the function f continuous on (- 0, ∞) where x2 – 36 if x 6 1 6…

A:

Q: 1 You are given the function f(x) = x2+7 f(x) is concave up whenever:

A: