12. What is f( + 1) if f(x) = –4x +17a-3x 4? O 4 -4x 17a2-4x O 4a 5 19x 6 | -4x 21a2 - 3x 6 -4 + 21x2 -20x-4

Q: 1 if x -2 18. f(x) = x + 2 %3D a = -2 1 if x -2 x+3 if x -1 a = -1

A:

Q: What are the critical points for the function f(x) = x³ + 6x² – 36x + 7 X = - 2 and x = 6 x = 2 and…

A:

Q: In Problems 21–32, tell the maximum number of real zeros that each polynomial function may have.…

A: "Since you have asked multiple questions we will solve the first question for you. If you want any…

Q: 2. If F' =fand f(x) = 18x 12x+ 2x, which of the following could be F(x) ? %3D %3D - (A) 3x° – 3x* +x…

A:

Q: 19. f(x) : х — 2 x² - 4 20. f(x) = х — 2 (2r 15 if v-

A:

Q: The antiderivative of the function f(x) : .4+7.5x³ is. -7.5 + 0.5x² + c -2 + 1.9x* + c -2 +1.9x³ + c…

A: To find the integration

Q: Given f(x) = 1 –(5+ 10x) + (5 + 10x)² – 27 (5 + 10x)³ then f'(x) =, %3D - (5 + 10z) – ( 5 +…

A: f(x)=1-32(5+10x)+94(5+10x)2-278(5+10x)3 Then f'(x)=0-(32×10)+(94×2×5+10x×10)-(278×3×(5+10x)2×10)…

Q: Let h(x) = f (X)g(x). If f (x) = In(3x² - - 4) and g(x) = 3x – 1, what is h' (x)? Select the correct…

A: Here, the given function is: h(x)=f(x)g(x)

Q: Solve the equation below giving an explanation. Thanks.

A:

Q: If f(2) = 15 and f (x) > 2 for 2 s x s 4, how small can f(4) possibly be?

A:

Q: 9. If f(x) = x2 - 2x + 5, what is f(x+h)? %3D A a2 -2x + h2 - 2h + 10 x2 + 2xh + h2- 2x 2h +5 C a2 +…

A:

Q: 1) If f(x) = - 2x, then f' (8) = A) B) D) 1 E) 3 3x -2 2) If f(x) = , then f'(x) = 2x+1 A) 2 -7 B)…

A:

Q: The function f(x) = 2x^3 - 27x^2 + 108x - 4 has two critical numbers. The smaller one is x = ? And…

A: Hereupon plotting we can see that horizontal tangent can be drawn at points x=3 and x=6.  Note: The…

Q: 14 7) If f(x) = T4x-5) find f"(x) %3D

A: Given function is- f(x)=14(4x-5)27We need to find f''(x)First we will find f'(x) f'(x)=ddx14(4x-5)27…

Q: If f(z) = 5.7x +6.9, then, f(x+h) is:

A: Given : fx =  5.7x+6.9

Q: If f (x) = x²cos-(x² – 4), what is f'(x)? 2x3 o f'(x) = 2xcos-'(x² – 4) – V 1-(x²-4)² 2x3 o f'(x) =…

A:

Q: 2 If f(x) = and g(x) then (g of)(x) is equal to x + 3 1 + 3x A x + 3 D 2x x + 3 2х 1 + 3x 2x

A:

Q: -x², 5х - 4, 4x* - 3х, 1<x<2 X <0 0 <x<1 If f(x) = then f(x) is discontinuous at x = Зх + 4, x 2 2…

A: f(x) is discontinuous at x if left hand limit not equal to right hand limit

Q: 2. Given : f(x) = {x² - 3, x+3 6, %3D X = 3

A:

Q: If f(x) = 2x² + 4x - 3, then f(x+h)-f(x) h 012x+ +2h)²+(4x+4h)−3−(2x²+4x-3) h 2(x+h)² +4x−3−2x² -…

A:

Q: If f(x, y) = (3x³ + 2y² – 12)', then fy is given by : 6. O 42 y (3x³ + 2y² + 12)° O 28 y (3æ³ + 2y²…

A: fy: Partial derivative of fx,y w.r.t. y Keeping 'x' as constant.

Q: 3 If f (2) = -5 and f'(2) = – find [f-1]'(-5). %3D 4

A: topic - derivative of inverse function

Q: Suppose 3x2 – 3x + 8 - f(x) : x (x2 + 4) Then A f(x) Bx + C | x² + 4 where A = and B %3D , and C =

A:

Q: If f(x) = 3x-1 +4 and g(x) = 4x-7, what is (f- g)(x)? %3D O A. (f-g)(x) = 3x-1 - 4x- 3 %D B.…

A:

Q: 17. If f(x - 1)+ 2/(1 — х) %3 3х, what is f(x)? А) -Зх + 1 В) х—3 С) -х +3 D) -3x – 1 |

A:

Q: (8) If f(x) = x² – 3x, what is f(x +h) - f(x) =? h (x² + 2xh + h²)-3(x+h)-(x²-3x) = 2x – 3 + h (x² +…

A:

Q: _6. If f(x) = 18x² and t(x) = 8x, find f(x). t %3D c. 4_ 9x d. 9 a. 9x 4 b. 4x 9 4x _7. When f(x) =…

A: Explanation of the solution is given below...

Q: Given f(z) 3D 1-홀 (7+ 3x) + 을(7+ 3x)2- (7+3x)" then f'(z) =. -을 + 꼴 (7+ 3z) -(7+3x)2+ | .... -글 +…

A:

Q: What are the critical points for the function f(x) = x³ + 6x² – 36x + 7. %3D

A:

Q: If f(x) = 3x² +5+ (4x – 3)* | , then f '(x) is - + 5+ (4x – 3)*]" [4(4x – 3)'] B. [3* +5+ (4r -…

A: Given:            fx=3x2+5+4x-349 Solve: f'x           ddxfx=ddx3x2+5+4x-349

Q: x'-x+2 If fx) =ア+7 6. , find f'(x). (5x-1) (A) (3x) (x'+7)(5x-1)-(x'-x+2)(3x) (x+7) (B)…

A: Given query is to find the derivative of the expression.

Q: 4. If f(x) = -6x and g(x) = -6x %3D 203 2x+3 and g(x) = 3x 5. If h(x) = %3D

A: The solution are next step

Q: 3. If f(x)=-4x+2 and g(x)=vx 8 find (fog\l12) 4. If f(x)=-3x+4 and g(x)=x find (gof)(-2) 5. If f(x)…

A: 3. Given f(x)=-4x+2 and g(x)=x-8f∘g(12)=fg(12)so now substitute g(12) in given…

Q: Derivatives question: finds f’(x)

A: Given function can be written as

Q: 5 2 7 . If f(x) = 3 + 4x · 2* + r", what are f"(0) and f"(0)? 3!

A: Given f(x)=3+4x-52!x2+73!x3

Q: 2 If f (x) =x² and g(x) =x – 5 then f(g(x))= x² + 25 x² – 25 O x²-5 O x² – 10x + 25

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

Q: What are the critical points for the function f(x) = x³ + 9x² + 15x – 8 %3D None x = -1 and x = -5 x…

A:

Q: Find (f - 9)(ӕ) if f(«) — 4г? — 5ӕ + 8 and g(z) — 203 + ӕ - 2 O (f - 9)(2) = 6æ² + 4x 6 (f - 9)(x) =…

A:

Q: Consider the following problem; max F(x1 ,X2) = x,x3 subject to 6x + 3x3 = 72

A: Solution is given below:

Q: Suppose 2<f'(x) < 4, for -1 sxs1. Then f(1)- f(-1) is between A) 4 and 8, B) 8 and 16. C) 0 and 4.…

A: Given  2≤f'(x)≤4 for -1≤x≤1Then We know thatf(1)-f(-1)2=f'(1) (by definition of derivative)We know…

Q: Find (f – 9)(x) if f(x) = V16z4 and 9(ax) = 3a² – 3x – 5. O (f – 9)(x) = x² + 3x + 5 O (f - 9)(m) =…

A: Given f(x)=16x4g(x)=3x2−3x−5

Q: 21. If f(x) = 2x - 1 and g(x) 3x + 5, what is f(g(5))? %3D %3D

A: Given, f(x)=2x-1 g(x)=3x+5 f(g(5))=?

Q: What is f'(3) if f(z) = z/2z - 2 I.

A: d(xn)dx=n(x)n-1

Q: 2 If f(x) = (x³ +3x)“, what is f'(æ)? O f'(x) = (x³ + 3x) O f (x) = (x³ + 3æ) (3a² + 3) O f'(x) = 2…

A: Follow the steps.

Q: In Problems 21–32, use Descartes’ Rule of Signs to determine how many positive and how many negative…

A: Use Descartes’ Rule of Signs to determine how many positive and how many negative zeros each…

Q: 4 If f'(x) = x³ x'-2x +x+2, then f has inflection points at 3. n X=0 X= -0.5 X-1 x-0.6 X-2

A: Point of inflection  Those points where cancavity changes called inflection points

Q: 21 If fx)3then f(x) O 2x-2-1 3x 2x-3r2-3 3x O 2x-3x2-3 6x 2x 3x+2 O 2x-x2-1

A: Find the derivative of the given function.

Q: f  f(x)=ln(7x^6−3x^2) and g(x)=(π3lne‾‾‾√+13log2(16))5e+x5+6x,  f′(1)=

A: f(X)=ln(7x^6-3x^2)         2nd question is not written proper please write properly and resend

Q: -8- -7 -6- 5- y = f (x) 3- -2 sy = g(x) LO 4-

A:

Q: The antiderivative of the function f(x) = -.9 + 10x³ 9. is -6 2.5x4 + c -6 + 2.5x4 + c -10 + 1.5x* +…

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.