Find the average rate of change of the function over the given intervals. ​f(x)=4x3+4​      a​) ​[2​,4​]    b​) ​[−5​,5​]

Q: Find the average rate of change of the function from X1 to X2. f(x)= -3x2-x from X1= 5 to X2= 6

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Q: Determine the average rate of change of y in the function y = 2x³ + 7x² + 2x - 3 er the interval…

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Q: Estimate the slope of the tangent line to f(x) = tax(x) at the point x = 9π/4

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Q: Find the average rate of change of the function between the given values of x. y = −5x − x2 between…

A: average rate of change= -7 for detail...go through the solution

Q: Find the average rate of change of the function on the interval specified for real number h. f(x) =…

A: We have to find average rate of change of the function f(x)=6xr+y on [x, x+h]

Q: Find the equation of the tangent line and the normal line at the point corresponding to the given…

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Q: Find the average rate of change of the function between the given values of x. y = −5x − x2 between…

A: We are given that : y = -5x - x2 We need to calculate the average rate of change of the above…

Q: find the tangent line of f(x)= 3x-4/x+1 at x=0

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Q: a. Find the average rate of change of f(x) = -3x³ + x -1 between [-1,0]. b. Find the Difference…

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: Determine the coordinates of the point(s) on the graph of f(x) = 5x ^3 - 2x ^2 where the tangent…

A: Our aim is to determine the coordinates of the points on the graph off(x)=5x3-2x2 where the tangent…

Q: 10) Using the First Derivative Test, what are the local extrema for the function 5(x)==x²+10 x³…

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Q: Find equations of the two tangent lines to the graph of f(x) = x² that pass through the point (1,…

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Q: Estimate the slope of the tangent line at the point x = 3, for f(x) = In(x). (Use decimal notation.…

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Q: Determine the equation of the tangent line and the normal line to the curve f(x)=x3 -3x2 +2x +2 at…

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Q: Find the average rate of change of f(x)=−x2+9x on the interval [1,6].

A: Given: The given function is, f(x) = -x2 + 9x  on [1, 6]   To determine: The average rate of change…

Q: Find the average rate of change for the function over the given interval. y = x3 - 3x2 + 5 between x…

A: The average rate of change of a function f(x) from x = a to x = b is

Q: Find the average rate of change of the function f(x) = x² - 2x + 3 between x = -2 and 2 = 4. Type an…

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Q: Using the First Derivative Test, what are the local extrema for the function s(x)=−23x3+10x2−48x−1?

A: Given Sx=-23x2+10x2-48x-1

Q: Find an equation of the tangent line and an equation of the normal line to the graph of x + 5 f(x)…

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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)?    Please…

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

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: Find the average rate of change of g(x) = 3x² – 2 between the points (-4,46) and (3,25) -

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Q: 12, for f(x) n(x) Estimate the slope of the tangent line at the point x (Use decimal notation. Give…

A: Given,

Q: Find the average rate of change of the function on the interval specified for real number h. f(x) =…

A: The average rate of function f(x) on the interval a,b is given by  average rate of change = fb-fab-a…

Q: Determine the function f(X) such that the slope of its tangent line is given by sqrt(3x+1) and the…

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Q: Use the first derivative test and the second derivative test to determine where each function is…

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Q: Find the average rate of change of the function from x₁ to X₂- Function x-Values f(x) = -3x³ + 7x² +…

A: Average rate of change is just an another name for slope. If f(x) be a function then the average…

Q: e average rate of change of the function from Function X-Values f(x) = -2x3 + 8x2 + x X1 = 1, x2 = 8

A: Given : fx = -2x3+8x2+x

Q: Find the average rate of change of the function on the interval specified for real number h. f(x) =…

A: The given function is fx=2x2+5. The average rate of change of a function f over the interval x,x+h…

Q: Apply the quotient rule and the derivative of cosh(x) to compute the derivative of the given…

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Q: What is the rule for calculating the derivative of a composite of two differentiable functions? How…

A: Let us we consider a function which is real valued function which is composite of of two functions…

Q: Show that the rate of increase in the slope of the tangent at a point on the curve y = 2x3 is 12…

A: Consider the given curve: Here the objective is to show that the rate of increase in the slope of…

Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = 4x − 5x2…

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Q: Find the average rate of change of the function on the interval specified for real number h. f(x) =…

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Q: Find the general anti-derivative of f(x) = 3. + Vx on a continuous interval. Please select file(s)…

A: topic - integration

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 of the function from x1 to x2. Function      x-Values f(x) = x2 −…

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Q: Show that a constant function f(x) = b has an average rate of change of 0. Compute the average rate…

A: Average rate of change of constant function fx=b Rewrite;              y=b…

Q: The slope of normal line (perpendicular to the tangent line) to the graph + = 3 at the point (1,1)…

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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: The maximum rate of change of the function 1 ----> at the point (1,-2) happens in direction of and…

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Q: Find the derivative car (x+y) = yrinx

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Q: 7. Find the slope of the tangent line at point (-2,2) on the curve flx) = 2x² + 3x. %3D

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Q: Find the equation of the tangent line and the normal line at the point corresponding to the given…

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Q: Find the equation of the tangent line to the graph of f(x) = In(-x) at x = x0 = -e'. =-e?. Equation:

A: As we know that the equation of the tangent line is: y-y1=mx-x1 Where 'm' is the slope. Given:…

Q: Use the fact that the derivative of the function f(x) =- is f'(x) = to find the equation of the…

A: We need to find the equation of tangent to the graph of f(x).

Q: 3. The normal line to the curve y = f (x) = 2x² at a point in the first quadrant passes through the…

A: Question is solved.

Q: Find the average rate of change of the function on the interval specified for real number h. f(x) =…

A: We will use the average rate of change formula. f(x+h)-f(x)h

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).