Locate the critical point of the function f(x) = -2x3 + 6x2 -3. Then use the Second Derivative Test to determine (if possible) whether they correspond to local maxima or minima. 5.

Q: Question 12 Find the derivative. y = 126x A (72 In 12)126x B (12 In 6)126x (C) (72 In 6)126x D (6 In…

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Q: 3x' +5 (3x° +5)* (6x)+(3x° +5) (3)(-3x - 4) (-3) -75-8x)

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Q: IN QUESTIONS 1-5, FIND THE DERIVATIVE. 3 1. y = Vx + cotx

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Q: I understand that the derivative of cosx is -sinx, but I need to show the work using trig…

A: We have to find the derivative of cos(x) by using definition of derivative by limit.

Q: 4. j' (x) = Va – 1

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: QUESTION 7 Find the second derivative. y%3D y = 4x 4 - 8x 2 8 8x 2 - 8 O 48x2 - 16 O 16x2 - 16 O…

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Q: To Calculate derivative at a specific instant we needed two points, so that we could subtract first…

A: The first derivative of a function f(x) at x=a  can be calculated as f'(a)=limh→0f(a+h)-f(a)h So, we…

Q: 10 dx 64-Г 3

A: It is known that  ∫0π2sinpt cosqdt=Γp+12Γq+122Γp+q+22. Here, Γx is the Gamma function.

Q: Match the following equations with their direction field. Clicking on each picture will give you an…

A: Given differential equations are 1. y'=2y+x2e2x2. y'=e-x+2y3. y'=2 sin (x)+1+y4. y'=y+2

Q: In each of the following problems, use the method of undetermined coefficients to find the solution…

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Q: which value of x gives the rectangle it's largest area? Show your reasoning.

A: The equation of the line in given figure passing through the points (0,3) and (9,0) is

Q: Preview Activity 1.1.1. Suppose that the height s of a ball at time t (in seconds) is given in feet…

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Q: In each of the following problems, use the method of undetermined coefficients to find the general…

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Q: 1.x²a 2. 2x¹-a

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Q: How would i find the derivatives of this inverse trig. problem? y = (1+Tan-1x)2

A: Given that the given function is

Q: Use the manual method of your choice (using methods only up to and including section 3.10) to find…

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Q: Match the following equations with their direction field. Clicking on each picture will give you an…

A: Given equations: 1. y'=2xy+2xe-x2 2. y'=yx+3 cos2x 3. y'=-2x+y2y 4. y'=2y-2 To Match: Each function…

Q: Sy' =2y+3 Ly(0) =3

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Q: B. f is not continuous at x =a C. f has a relative maximum at x = a D. f is continuous but not…

A: Here, we have given a function now we have to calculate the points where the function has point of…

Q: Consider the differential equation y" + ay' + By =t+e“. Suppose the form of the particular solution…

A: Given differential equation is, y''+αy'+βy=t+e4t The solution of above equation is,…

Q: Find the derivative of ?=1?‾‾√y=1x. (The correct answer might not be in simplified form.)

A: Explanation and solutions is given below....

Q: 6. In(x*y?) %3D х* +уз 7. У- Arccos(e2x)

A: Given In(x3y2)=x2+y3y=cos-1(e2x)we need to find the second derivative of the given equation

Q: dV E = dx d(a+bx) E = - dx E = -(b)

A: Consider  V=a+bxE=-dVdx

Q: Determine the derivative -d/ 4 8 +³−1 - 17x y= y = 25 x-5 x+6

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Q: 8. y= sec® (e-sin?x) |

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Q: Problem: A person who is 6 feet tall is walking away from a lamp post at the rate of 40 feet per…

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Q: How did you get from step 2 to the solution? I dont understand your example. Am I taking the…

A: The answer is in step 2.

Q: L08. Let f(x) = (x² + 1)(x³ + 3). Find f'(x) in two ways: (a) by multiplying and then…

A: 108. fx=x2+1x3+3109. fx=1+x24

Q: In each of the following problems, use the method of undetermined coefficients to find the general…

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Q: Determine the derivative -d/dv y = 2x³ + 5x - 6 y 1 x² 3x 6x³ + x² − 10x − 3 -

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Q: What is the normal line to the curve given by x – y = Vx +y at the point where y =1?

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Q: respect to x without using the formula. Use y instead of show differentiation. Use / for fraction,…

A: we will find the required.

Q: According to the following data: (0,0), (0.2, 1), (0.4, 3), (0.6, 5), (0.8, 7), (1.0, 5), (1.2, 3)…

A: 6hD=-9i-2-10i-13i-2i+14i+2 0,0, 0.2,1, 0.4,3, 0.6,5, 0.8,7, 1.0,5,1.2,3

Q: dy D. y = sec(x? + 4). Find dx dz E. z = 3x² cOs x . Find dx

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: