4. If f(x) = x2 – 7x, find the difference quotient and simplify.

Q: A liquid form of penincillin manufactiured by a pharmaceutical firm is sold in bulk at a price of…

A:

Q: 1. How to define the function, f(x, y) = 15x+4x*y+15y 3x+3y to make it a continues function?

A: We have to find the given function is continuous.

Q: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

A: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

Q: Suppose you have a function y = f(x) such that the domain of f(x) is 1 ≤ x ≤ 5 and the range of f(x)…

A: Given: The domain of fx is 1≤x≤5 The range of fx is -3≤y≤6

Q: 25. If f(x) = 3x² – x + 2, find f(2), f(-2), f(a), f(-a),

A:

Q: 2. Determine f'(1) for the function f(x) = (8x – 6Vx5 + 3) (x² – 9x² +) -

A: A detailed solution is given below

Q: 2) If f(x) = , then f() : 2x + 3 6x – 5 SHOW ALL YOUR WORK =

A:

Q: Calculate R3 and L3 for f(x) = x2-8x+2 over [1,4] .

A:

Q: Determine the values of x for which f (x) = 1x − 4 is increasingand for which decreasing

A: fx=1x-4 Differentiating with respect to x, we get f'x=-1x-42    ∵ddx1x=-1x2

Q: Зах + 3 for x -2

A:

Q: Differentiate the function. y = In|4 – x – 4x²| (-1– &r) In| (4 – x – 4x?)|| y' = — х — 4х*

A:

Q: f(x) = (1 – x²) |

A: Given query is to draw the function.

Q: Find the value of the constant k that makes the function continuous. 2x-2x-12 if x+3 g(x) = , x-3 kx…

A:

Q: If f(z) = (3z -3)(2-22), use the product rule to find f'(0). %3D

A:

Q: # 3) Find f(x) if f'(x) = 9x2 – 12x – 5 and f(2) = 4 -

A:

Q: When the qiven function f(x) = cx^3 - 3x^2 + dx - 4 is divided by (x+2), the remainder is -34. When…

A:

Q: Let f(x)=3x^2+7x-4 and g(x)=9x^2-5x+1. Which equation shows h(x), where h (x)= f(x)-g(x)?

A:

Q: Find the slope of f(x) = -3x2 – 6x at x = 1

A:

Q: 2 If f'(x) = 3x2 - and X f(1) = 0, find f (x)

A:

Q: 2. If f (2) = 10 and f' (x) = x²f (x) for all x, find f"(2).

A:

Q: Suppose z is implicitly defined as a function of x, y, by means of the equation: z4+8zx=3x2+12y2…

A:

Q: The linear functions m(x) and n(x) are perpendicular to each other and intersect on the x-axis. If…

A: Two lines with slope m1 and m2 are perpendicular to each other if m1m2=-1 Given: m(x)=4x+48 Let the…

Q: 1. If f(x) = 5x4 - 6x² + 4x - 2 find f'(x) and f'(2).

A:

Q: Calculate R3 and L3

A:

Q: Find the most general antiderivative of the function. f(x)= 8x-11/10

A:

Q: Suppose we want to form an interpolant at equally spaced points xo = 0, x1 = h, and x2 = 2h of the…

A:

Q: (b) f(x), where f(x) = (2x +1 x 1 Evaluate

A: We have to find the value of the integration between the limit 2 to 5.The function is piecewise…

Q: 4. Given that f'(x) = −6x² + x + 12 and f(1) = 7, find f(x).

A: Given : f'(x)=-6x2+x+12f(1)=7   To Find : f(x)

Q: Find the value of the constant k that makes the function continuous. 2x - 2x - 12 if x 3 g(x) = X- 3…

A: For function to be continuous

Q: 3. For f(x) = 15x²-3 16x²+9x+8 As x → ∞, y → || As x →∞, y →

A:

Q: What value of b completes the function f(x) = −x2 + bx + 1?

A: We have to find the value of b that completes the function f(x)=-x2+bx+1.

Q: 2. If f"(x) = 4sinx+16cosx, f(0) = 6, f'(0) = 1, find f(x) and f(4).

A:

Q: Calculate R_5 for f(x)=2x^2+8x over [-1,1].

A: Given: fx=2x2+8x The interval is -1, 1

Q: If f(z) = 19z+ 24, find f'(-3).

A: Here, the given function is: f(x)=19x+24

Q: 1. If f(x) = 2x – x² and g(x) = |x – 3|, find the value of f(-2) + g(-2)

A:

Q: 6. If f(x) = 10x – 5, what is f-1(ƒ (3))?

A:

Q: The function f (x) = (x + 6)³ – 2e** has two roots between x = -7 -

A: Solution of the problem as follows

Q: f(x) = Vxe-x/2 is inc decreacing

A:

Q: 7.If f(x)= 2x – 1 and g(x)= x² – 2x, find f(3)/g(2). -

A: Given fx=2x-1 and gx=x2-2x. To find: f3g2 Solution: Finding f3.  f3=2·3-1=6-1=5 Now, finding g2.…

Q: 5. use the four- step procedure to find f'(x) 1 b) f(x)24x 2 a) f(x)

A: Use four-step procedure to find derivative of f(x).

Q: Find where the function f(x) = 3x4 − 4x3 − 12x2 + 5 is increasing and where it is decreasing.

A: Topic = Functions

Q: I noticed that the difference quotient is always zero if f(x) = c, where c is any constant.

A: Difference quotient is also known as definition of limit. f'x=limh→0fx+h-fxh Given function is fx=c,…

Q: 1. If f(x) = 5x4 - 6x² + 4x2 find f'(x) and f'(2).

A:

Q: Find the deivative of f(x) = Sec(4x72x)

A: Solution: The objective is to find the derivative of the given function

Q: Find the value of the constant k that makes the function continuous. 2x - 3x- 20 if x#4 g(x) = x-4…

A: A function f(x) is continuous at a point x = a iff:

Q: Find the interval in which the function given by h(x)= 4x – 6x – 72x + 30 is decreasing.

A:

Q: Intergrate f(x)=15x^4/x^5+7 with respect to x

A: Note:- Here, Given function is not completely, defined as it can be 15x4x5+7 or 15x4x5+7 other cases…

Q: Find f(4) using forward, backward and central difference of: (3 – 2x)² f (x) : |- x2 Step size = 0.2

A:

Q: 1 If f (x) = 2x² + 4x and g (x) = , find . 2x

A:

Q: 3 Let f(x) = 4.x² 5 and g(x)= 3.x + 7, find. -

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.