1. Use the first derivative test to find the local minimum and maximum points of the graph of f(x) = x²+1'

Q: 4. Find the equation of the tangent line to the graph of f(x)= 2x² – In Vx at x = 1.

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Q: 2. Find the derivative of a function at a certain number using the formula. f(x) – f(xo) f'(x) = lim…

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Q: Assumee thát ic COst C(x) = 25,600 + 100x + 0.01x² dollars to manufacture x 32GB iPods in a day. t…

A: given cost functio cx=25600+100x=0.1x2

Q: 10. Find the equation of tangent line to the graph of f(x) = 2x – x³, at the point(-1, –1). %3D

A: Find your answer below

Q: 1. Find the slope of the tangent line to the graph of f at x = 4, given that f(x) = -x2 + 4Vx.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 3. Suppose the function f has second derivative f"(x) = x2(x – 3)(x+2)*(? – 1). = T- (a) How many…

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Q: 8. Suppose the derivative of the function y = f(x) is y' = (x – 1)*(x – 2)(x – 4). At what points,…

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Q: • Show that both of the functions f(x) = (x − 1)^4 and g(x) = x^3 −3x^2 + 3x+ 2 have stationary…

A: given functions fx=x-14gx=x3-3x2+3x+2 (A) to show both have stationary point at x=1 differentiate…

Q: 4. Find the equation of the tangent line to the graph of g(x) = v2-x at x =-7 %3D

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Q: Find an equation of the tangent line to the graph at the given point .

A: Given: fx=4xx2+6 We need to find the equation of the tangent line to the graph f(x) at 2,45

Q: The slope of the line tangent to the graph of y = In(x²) at x = e² is %3D

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Q: 4. Find an equation of the line tangent to g(x) = 3x² - x +1 at x= 1.

A: Given function

Q: 14. Find the equation of the line tangent to the graph of f(x) = 2x3-x + 1 at x = -1. %3D

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Q: 4. Given f (x )=x'-12x +1. Use the second derivative test to determine the local extremum off (x).

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

Q: Consider a function y =f(t) with domain (0. 1, 4. 2). Use the graph of the derivative function,…

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Q: 3. Find the equation of the tangent line to the graph of f (x) =7-3x-x at x= 1 %3D

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Q: 10. (a) Find an equation for the line tangent to f(x) = x³ + 4x² at the point x = 1.

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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: 2. Find the points on the graph of f(x) =- where the tangent line is horizontal. x2+2

A: Given f(x)=xx2+2we want to find the point on curve where tangent is horizontal

Q: 2. Find the equation of the tangent line for the function 2 f(x) = x2 + - 3 at a = -2

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Q: 4. Find the equation of the tangent line to g(x) 8 at x = 3 |x²–1

A: The function is given by gx = 8x2-13 To evaluate: The equation of the tangent line to the graph of…

Q: (5) Find the local maximum and minimum values of f(r) = 1+3x2 – 2.r using either the First…

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Q: Find the equation of the line tangent to the graph of f(x)=−3cos(x) at x=−π3

A: As we know that: The first derivative of the function is equal to the slope of the tangent line to…

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

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Q: 2) Find the point(s) at which the graph of f (x) = has a horizontal tangent. x2+1 %3D

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Q: 3. Determine the gradient of the tangent at a point (2, 5) to the XY graph with the implicit…

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Q: 11. Use the limit definition to find the derivative of f(x) = x² -2 x. 12. Find an equation of the…

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Q: 2. Given the graph of derivative f'(x), find: a) Any interval (s) where f(x) is decreasing b) Any…

A: the function is decreasing when  as we can see from the graph,  on the interval  and  which means…

Q: 8) Find the equation of the tangent line to the graph of g(x) x3 7 at x = 2. -

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Q: 15 Find the equation of the tangent line to the graph of f(x) at the point where x = 2 Vx3 – x + 3

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Q: 1) Find the slope of the tangent line to the graph of f (x) = x3 + x at x = 3.

A: Application of derivative problem

Q: 4) Determine the equation of the tangent line to the function 2 f(x) = x at the point (3, 9).

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Q: the value of x at which the FOC is satisfied give us the ........(maximum/minimum) of the function…

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Q: 4. Find the tangent line to the function f(x) =;xVx² + 5 at the point (2,2).

A: Tangent line of a function:  Differentiate the equation of the curve Substitute the value into the…

Q: Find the critical points for the following function. Then use the second derivative test to…

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Q: #4) Given the function f (x) =x³-x² +2x- 1. Use the second derivative test, where applicable, to…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 3 Consider the function f(x) = 2+ 1+ (x+1)? Compute the derivative f'(x) . Determine all of the…

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Q: 2 Determine the equation of the tangent line to the graph of f(x) = Vx-12x at the point where x -3.

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Q: 8) Find the equation of the line tangent to the graph of f(x) = x – :- at the point where x = 1.

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Q: 2) Find the tangent line to y2 = x at the point (4, –2).

A: Given: y2=x…

Q: In our last class discussion we found that a function y(x)= x* indicated by taking y"(x) = 0 that…

A: Definition: The first derivative of a one-variable function is zero at the points called stationary…

Q: 15. Find any local maximum and local minimum values , then sketch each curve by using first…

A: We use first derivative test to find local maximum and minimum

Q: 1. Find the equation of the tangent line to the graph of f (x) = x²e-* at x = 1. %3D

A: The given function is: fx=x2e-x In order to find the slope of the given function, find the…

Q: 3- Suppose that the second derivative of the function y = f(x) is y" = (x + 1)(x - 2). For what…

A: 1)y'' = (x+1)(x-2)2)y' = (x-1)2(x-2)(x-4)

Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: The given function is fx=1+x. The derivative of the function is, f'x=1. At point a = 8.1,…

Q: 15. Find any local maximum and local minimum values , then sketch each curve by using first…

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Q: 24. Consider the graph of y = Use limits and 1+ eax first derivatives to determine how the shape of…

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Q: 3. Find the siope of the tangent line that crosses through the point (3, 7) along the 2 curve f(x)=x…

A: Given :f(x)=x2-x+1

Q: 1- Find the equation of the tangent to the curve y= 2 sin x+ cos2x at the point x = n. 2- Find the…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Find the x-value for all relative extrema of f(x) using the first derivative test. 1+x + x² f(x) =…

A: Given: The function is  fx=1+x+x2x2+x-2   To determine: The x value for all relative extrema of f(x)…

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.