Suppose that the functions s and t are defined for all real numbers x as follows. s s (x) =x+1 1 (x) =2x² Write the expressions for (t+s) (x) and (t-s)(x) and evaluate (t-s) (2). (* + s)(x) = ] (1 - s)(x) = 0 %3D ? (1-s)(2) = 0 %3D

Q: -1 if f(x) = xtan ,"x,find f' (/3 )by first principle

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Q: Find critical number of f(x) = 5x^2-8x+1

A: Given,          fx=5x2-8x+1

Q: In the function:  f(x)= (4x^2)/((x^2)+4)  What are the critical numbers of the function?  Where is…

A: Given function

Q: - Find f '(x). f(x) = - 3 In x+ 11x² - 9 f '(x) = . Find f '(x) f(x) = -9-5x + 4 ex f '(x) = . Find…

A: Solve for the derivative

Q: 38 Find the critical numbers of the function. 25. f(x) = x³ + 3x² – 24x %3D -

A:

Q: B. Find the extreme values on the given closed interva 1. f(x) = 4x - 3; [1,5] 2. f(x) = x + 8;…

A: follow next step

Q: In Problems 23–38, for the given functions f and g, find:(a) f ∘ g (b) g ∘ f (c) f ∘ f (d) g ∘…

A: In Problems 23–38, for the given functions f and g, find: (a) f ∘ g (b) g ∘ f (c) f ∘ f (d) g ∘ g…

Q: The function f(x) = 2x³ - 39x² + 216x 3 has two critical numbers. The smaller one is x = and the…

A:

Q: Find a polvnomial f(x) of degree 4 with real coefficients and the following zeros. 3,-4, 2+i 1) - 0…

A: Given,  The zeroes of the 4 degree Polynomial f(x) is 3, -4 , 2+i and 2-i.

Q: Find all critical numbers for the function f(x)=1/(x^2-9)

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Q: 7. Find the critical numbers of the function. (1) ƒ (x)= x³ + r² – r

A:

Q: Show that f (−1) = f (1), but that there is no point in (−1, 1) where f (0) is zero. Why does this…

A: Given: fx=1-x2/3 So, f-1=1--12/3=1-1=0 Also, f1=1-12/3=0 Thus, f-1=f1

Q: Find critical number of f(x) = x^2 - 6x + 8

A: To find critical number of f(x) = x^2 - 6x + 8

Q: Find the critical numbers of the function. f(x) = 3x + 4x3- 12x2 %3!

A: Given function is f(x)=3x4+4x3-12x2. The critical number of a function f is a number c in the domain…

Q: Find the critical numbers of the function f(x) =x^6/5-12x^1/2

A: In the given question find the critical point of the given function: f(x) = x^(6/5) - 12 x^(1/2)

Q: Find critical number of f(x)=x^3-6x^2

A: Given: f(x)=x3-6x2

Q: 15. Given , find f- (x) = Vx+ 7 and the domain of f-1 (x). Of-" (x) = x³ +7 with domain for f-l (x)…

A: In the question we have to find inverse of the given function and domain of the function.

Q: Find all critical points for f(x)=x²-x² - 2x + 1.

A: Our Aim is to find all the critical points for f(x)=x3-12x2-2x+1 -(i)

Q: Find the critical numbers of the function

A: We first find the first derivative using the power rule

Q: 1. Find the absolute max/min values of f(x) = 3x – 12r + 5 on the closed interval (0, 3).

A: Given the functionf(x)=3x2−12x+5,[0,3]

Q: Show that when x increases from 1 to 1.25 and when it increases from 2.75 to 3, the value k of grows…

A:

Q: Find the critical numbers of the function.   f(x)  = 2x3 - 3x2 -36x

A: Critical numbers are the numbers for which f'(x) = 0

Q: 5. Show that the function f (x) has roots between (0,2) x² + 2x – 3 f(x) x - 1

A: To show the f(x) has roots between a and b we have to show that

Q: Find the critical numbers of the function.

A: Let f be defined at k if f'(k)=0, then k is a critical number of f.Since, the function is given by…

Q: find the critical point for the function f(x)=2 x3+3 x2 - 72x+ 14 %3D O None O 4,3 -1,2 O 3,-4

A:

Q: Suppose that 2 ≤ f '(x) ≤ 3 for all values of x. What are the minimum and maximum possible values of…

A: Given , Suppose that 2 <= f’ (x) <= 3 for all values of x. The minimum and maximum possible…

Q: Find all the critical numbers for the function g(x) = ¼ x4 - x3 - 5x2

A:

Q: Find all critical numbers of the function f ( x ) = 4 x 3 + 6 x 2 - 72 x + 9

A:

Q: 4.x +1 1 with f'(x) = 1/ 56x2 - 156x + 115 14x – 19 - - 3. Let f(r) = and f"(x) 4 %3D 3 5 Vr2 – 3x +…

A: To find the points on which it is concave up or concave down

Q: g(x) = x' + 3 x² – 24 x

A: The point x=k is said to be the critical point of the function f(x) if Case 1 : f(k) exists and…

Q: f(x) = x3 + 5x² + 2x

A: Given: f(x)=x3+5x2+2x

Q: Find the critical numbers of the function. f(x) = x³ + 3x² – 24x

A:

Q: * Find all critical numbers for the function: f (x) = (9 – x² ) O {-3,0,3} {0} {3} O {-3,3}

A: Take the derivative of the given function than equate to zero and solve for x. These values of x…

Q: 2. What are the critical numbers of the function: f(x)=(x² - 4) A. X=0, x=2 and x =-2 В. X30 only С.

A:

Q: Find all critical points for f(x)=x²-x²-2x+1.

A: Critical points of the given equation is x=-2/3,1

Q: Find critical number of f(x) = x^2-7x+8

A: Given function f(x) = x2-7x+8 The critical number is the value of x which makes derivative of f(x)…

Q: Find the critical numbers of the function F(x) = x/5(x - 9)²

A:

Q: 13,4) f(x.y) =In(x + x² +y² If Find x

A: f(x,y) = ln (x+x2+y2)∂f∂x=∂ ln (x+x2+y2)∂x=1 (x+x2+y2)×(1+12x2+y2)×2x

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: We use the quotient rule, product rule, and chain rule of differentiation to check the claim of the…

Q: 5. Show that the function f (x) has roots between (0,2) x² + 2x – 3 f (x) = X - 1

A: Given that

Q: Find critical number of f(x) = 4x^2 + 8x -1

A: We have to find critical number of  f(x) = 4x2 + 8x - 1 To find critical number, differentiate f(x)…

Q: 2. Consider the function а(т — 2) Vx +2 – 2 - if x 2, 2x 2 x² - where a, b, c are real numbers.…

A: Given function is  f(x)=a(x-2)x+2-2   if x<2b                     if x=21x-2-cx2-2x  if x>2…

Q: 3. Find the critical numbers of the function g(x)= 5x -8.

A: Given:

Q: Find the critical numbers of the function. f(x)=32x-2x^2 x=

A: