If fx) is a differentiable function such that f(-2)=-1 and g(x)-f(3x+1), then what is g'(-1)?

Q: If ƒ(x) = x^n, n>=1, show from the definition of the derivative that ƒ′(0) = 0.

A: Given,

Q: 5. Why does it make graphical sense that the derivative of aconstant is zero? That the derivative of…

A: Derivative of a function is a slope of function on given point, or derivative is a rate of change of…

Q: Find the derivative of the function by the limit process. f(x) = x2 - 2 %3D f'(x) = 2x %3D Need…

A: Apply Limit rule

Q: Determine the derivative of the cube root function f(x)=3√x using the limit definition.

A:

Q: Find the relative extrema of f(x) = 8+ 126x – 7x2 using both first and second derivative tests. f…

A: If second derivative is less than zero then there is relative maxima.

Q: Consider the function f(x)  whose second derivative is f"(x) = 10x+4sin(x) . If f(0)=2  and f'(0)=3…

A:

Q: Find the derivative by the limit process. f(x) = 11 – x2

A: We have to find the derivative by the limit process where f(x) = 11 – x2.

Q: Give an example of a function f (x) that has one  positive derivatives on the range (−1, 0) and a…

A:

Q: Use the limit definition of the partial derivative to verify the formulas

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Let f(x)=," 1 Use the definition (first principle) to determine the 1-x derivative of ƒ(x).

A:

Q: find the derivative of f(x) = (x²+4)(3x³ - 2x) at the point x = - 3[ use product rule] %3D B.

A: We have to find the derivative

Q: Find the derivative of the transcendental function. y' = y = 6e* x² +8 6(x²–2x+8)ex (x+8)²

A:

Q: Use the limit definition to calculate the derivative of the linear function.            f(x) = 12

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: Consider the function f(x) whose second derivative is f''(x)=5x+3sin(x) If f(0)=2 and f'(0)=3 what…

A: Given : f''x = 5x + 3sinx

Q: Is this calculus statement true or false: "We can determine that h(x) =x^4 has a minimum at x= 0…

A: Given function is  Then x=0 is critical point of h as h'(0)=0, but also h''(0) =0  Therefore,…

Q: Find the general anti-derivative of f(x) = + Vx on a continuous interval.

A:

Q: Find the critical coordinates of f(x) = x³ – 3x² + 8x + 1. Then, distinguish the local maximum and…

A: Given function is  f(x) = 13x3-3x2+8x+1                 ....(1) Differentiate with respect to x , we…

Q: 1.f(0) = (금x* + 3)" %3D

A:

Q: Find the derivative of f(x) = √x^2 + 1 at a = 2, using the limit definition (i.e. first principles)

A:

Q: Use the second derivative to find the location of all local extrema for f (x) = x + x2 – x3, -

A:

Q: A) Consider the function f(x) whose second derivative is f"(x)=4x+3sin(x). If f(0)=4 and f'(0)=4,…

A:

Q: Find the derivative of g(x)= (x+1)/(x+2) using th limit definition.

A:

Q: Find all the critical points of f(2z, v) = - . 1 + 4x – xy? and classify them using the second…

A: The given function is;  f(x)=-x3/3 +4x -xy2.

Q: Give an example of a differentiable function ƒ whose first derivative is zero at some point c even…

A:

Q: Is the function f(x) = |x| cos x differentiable at the point x = 0 ? (Use definition of the…

A: if lim∆x→0f(∆x+x)-f(x)∆x doesn't exist then not differential

Q: Find the derivative by the limit process. f(x) = 10 – x2 %3D

A: We know that the derivative of a function fx is given by:f'x=limh→0fx+h-fxh

Q: Analyze the stationary points of f(x) = x2ex by applying the second-order derivative test.

A: Stationary points are occurred where the first derivative of the function becomes zero. If the Value…

Q: Find the derivative and simplify exy -x² = 4Y² %3D

A:

Q: Is the functionf(x) = |x| cosx differentiable at the point x =0 ? (Use definition of the derivative)…

A:

Q: Find the derivative of the function by the limit process. f(x) = 3x- 1 - (x), J

A: fx=3x-1

Q: 2) Use the definition of the derivative, f'(x) = lim Ax-0 derivative of f(x) = 5x² + 3. f(x+Ax)-f(x)…

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Q: 6. Use the definition of derivative to find f'(x) if f(x) 3D х2 — Зх — 4

A:

Q: Compute for the derivative of the function f(x)= Arctan (csc2 (3x2/3))

A: Some derivative formulas: ddxtan-1x=11+x2 ddxcscx=-cotx cscx Chain rule of derivative:…

Q: Find the derivative of the function by the limit process. f(x) = 7x – 6 %3D

A: The derivative is calculated using the limit process as follows. f'x=limh→0fx+h-fxh Now, fx+h=7x+h-6

Q: Find the critical value of f (x) = vx² + x – x using the second derivative test. %3D

A:

Q: are differentiable at a, then prove the sum and product rules for derivatives. If f, 9

A:

Q: Зx+1 5. f(x) %3D 3x2+2

A: f(x)=3x+13x2+2Differentiate…

Q: 2x 3, Use the limit definition of derivative to show that f(x) is differentiable at x2 – 3, r > 2 x…

A:

Q: Consider the function f(x) whose second derivative is f''(x)=2x+3sin(x). If f(0)=2 and f'(0)=4, what…

A:

Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

A:

Q: How does the partial derivative relate to the limit of a function of two variables?

A: Solution

Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

A: The given Revenue function R(x)=23x3-40x2-450x.  Task: To maximize this revenue function.

Q: Find the derivative of the function f(x) = v4-x2 by definition

A: The given function is f(x)=4-x2 The definition of the derivative is given by: If a function f(x) is…

Q: Use the definition of partial derivative of a function f(x, y) = 3x² – xy? to illustrate fi and f2 '

A:

Q: find the derivative by the limit process. f(x)=14-x^2

A: Here we find the derivative by the limit process fx=14-x2

Q: A company has identified that the revenue R for a particular product is given by the equation R(x) =…

A:

Q: Consider the function f(x) whose second derivative is f''(x)=2x+7sin(x). If f(0)=3 and f'(0)=3, what…

A: to find f'(x) integrate the given function c=integrating constant. Then plug x=0 and f'(0)=3 and…

Q: Find the derivative of the function y = 3x? – 4x + 7 using limit definition.

A: Given: y=3x2-4x+7

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.