For the function h(x)= x^3-3x^2-1, determine the equation of the normal line at x=2

Q: Calculate the length of the tangent line, normal line, sub-tangent and subnormal from: a. xy² = 18…

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Q: Find the slope of the line normal to the graph of y=secx at x=π/4

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Q: What is the First Derivative Test for Local Extreme Values?

A: What is the First Derivative Test for Local Extreme Values?

Q: Evaluate the second derivative at this critical number.

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Q: the tangent line  to the graph of y=lnx\x is perpendicular to the line x=7 at the point where?

A: The line x = 7 is perpendicular to x axis. Hence, it's slope is infinity. The tangent line that is…

Q: How can you sometimes graph the derivative of a function when all you have is a table of the…

A: We can draw the graph of derivative of a function using the values given to us in table of of the…

Q: y = 2x' - x' +x+1 when x =1

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Q: Show that the slope of the normal line to the curve y = 5 /(3-7x)^3 is never positive.

A: Given the equation of a curve is y=53-7x3. This can be written as y=53-7x-3. Differentiating it:…

Q: Use differentials to estimate the value. estimate =  exact value =

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Q: find the derivative of the function  y'=ln(squared root of x^2-4) and  y=ln IsinxI

A: The given function is y=lnx2-4. Obtain the derivative as follows.…

Q: Can the instantaneous rate of change be different than the average rate of change in the same…

A: We describe that the instantaneous rate of change be different than the average rate of change in…

Q: State the Second Derivative Test

A: Second Derivative Test:   This is used to find local extrema.

Q: find anti derivative.

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Q: Estimate the average rate of change from x = 1 to x = 4. %3D

A: average rate of change of f(x) on a,b=f(b)-f(a)b-aHere a=1 ,  b=4From graph f(1) = 5 ,  f(4) = 4

Q: Find the area of a triangle bounded by the y axis, the line f(x) = 5 - -2, and the line 4…

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Q: find the sLope Of a tangent line hCx) = x +44 iz

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Q: What is the equation of the normal line to the curve 2x3-2y3-9xy=2 at the point (0,1)?

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Q: Explain how to find the tangent line and normal line equation when the slope is undefined?

A: It is given slope at the point is undefined say the point is (x1, y1).  The equation of tangent at…

Q: Determine the anti derivative of the function.

A: Given Data: Function: fx=2x35+10x5-74x Similified the given function f(x).…

Q: what is the equation of the normal line to the curve 2x3+2y3-9xy=2 at the point (0,1)?    Please…

A: Given: 2x3+2y3-9xy=2 To Determine: Equation of the normal line

Q: Determine the derivative of y. アミeV10x+5

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Q: Determine the derivative of 6x log3(x)

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Q: What is the slope of the normal line to the graph y= -cosh(2x) at x= ln 2

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Q: Find the equation of the tangent and normal line of the function f(x)=√2x-1 at the point (5,3)

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Q: The slope of a nonvertical line is the average rate of changeof the linear function.

A: Given, A nonvertical line with any slope m equation of line is, y=mx+c slope of line is m=dydx for…

Q: Explain the relationship between the slope and the derivative of ƒ(x) at x = a.

A: Given function is  fx at x=a

Q: Brd Derivative OF y=-Jin3x

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Q: The number of live births recorded and the number of infants died in a town during a given period…

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Q: Use linear approximation to approximate the value of 65 without the need for a calculator.

A: This question can be solved using the concept of linear approximation.

Q: Find the anti-derivative of

A: Answer and explanation is given below

Q: he slope of the tangent line is 0. Is the slope of the normal line is undefined? If yes, how can I…

A: Consider the given slope of tangent line is 0

Q: How to solve for the second derivative?

A: The objective is to solve for the second derivative. Consider a function fx=3x4

Q: Find the most general anti-derivative

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Q: Find the slope of the normal line y^2=1-x^2 at point (2,1)

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Q: average rate of change

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Q: Find the derivative of the function. f(x) = /5 +x sec x [5+x secx

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Q: Find the equation of the normal line to the curve y= 2x -x+4 at point when x=1.

A: The solution is given as

Q: Find the average rate of change and the equation of the secant line for 2x f (x) = from -1 to 3. x²…

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Q: Find the slope of tangent line for the equation x^2+y^2=5 on (1,2)

A: The given equation of the line is,

Q: What is the relationship between the secant line, slope of the tangent line, derivative of a…

A: Solved below

Q: Calculate the derivative of h(x)= square root of x+1 when x=8 using alternate difference quotient

A: derivative of h(x)= square root of x+1 when x=8 using alternate difference quotient

Q: y = √√2x, x=2 yaxis 17 x-axis

A: Given that y= √(2x) and x= 2 and we find equation of tangent line and normal line at the given…

Q: Calculate the length of the tangent line, normal line, sub-tangent and subnormal from: a. x²+ y²-4x…

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Q: The slope of the tangent line is 0. Is the slope of the normal line is undefined? If yes, how can I…

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Q: What is the difference between a derivative and an integration?

A: We have to state the difference between a derivative and integral.

Q: Find the average rate of change of the function between the given values of X.  y=-5x-x^2 between…

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Q: Find the average rate of change of between the points on the function whose coordinates are (1, 3),…

A: Given points are (1, 3) and (2, 16).

Q: Find the derivative of the function at Po in the direction of A. txу) - - ху + у, Р,(10, - 2),…

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