Consider the function f(x) = 2x – 12x? mean slope of the function on this interval. 30x + 3 on the interval -5, 10|. Find the average or By the Mean Value Theorem, we know there exists a c in the open interval (-5, 10) such that f'(c) is equal to this mean slope. For this problem, there are two values of c that work. The smaller one is and the larger one is

Q: Consider the function f(x) = 2x 72x + 6 on the interval - 4, 7. Find the average or mean 3z2 slope…

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Q: What are the values f(4) and f 0 (4)

A: Given Data: Graph: y=fx Point 1: Ax1, y1=A4, 3 Point 2: Bx2, y2=B0, 2   The value of f4 will be…

Q: Consider the function f(x)=2x^3-15x^2-36x+8 on the interval [-4,7]. Find the average or mean slope…

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Q: Consider the function f(x) = 2x° – 12x – 72x + 3 on the interval [- 4, 7. Find the average or mean…

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Q: 7. Find the average rate of Change of f(x) = 2x2-7 on the interval [2, 2 + t].

A: Consider the given function, fx=2x2-7 At x = 2+t, f2+t=22+t2-7=24+4t+t2-7=8+8t+2t2-7=2t2+8t+1 At x =…

Q: For which value(s) of x does f(x)=8x3/3 +5x2 −10x+15 have a tangent line of slope −7? If there is…

A: We have been given a function and we need to figure out the x coordinates of the points where…

Q: Find f′(x) and find the equation of the line tangent to the graph of f at x=3.   f(x)=7x/2x

A: Given query is to find the equation of tangent line to f(x) ate x=3.

Q: Find the average rate of change of the function from x₁ to x₂. Function x-Values f(x) = -2x³ + 5x² +…

A: Average rate of change of function y=f(x) from x1=a to x2=b is given by f(b)-f(a)b-a

Q: Consider the function f(x) = 4x° 3x on the interval – 4, 4|. Find the average or mean slope of the -…

A: Given Data: Function: f(x)=4x3-3x Interval: [a, b]=[-4, 4] From mean value theorem, The mean slope…

Q: Given f(x) = 3x2 + 2x - 5, the average rate of change of f(x) with respect to x for the interval…

A: Given that, f(x)=3x2+2x-5 We need to find the average change of f(x) with respect to x for the…

Q: Find all points on the graph of ​f(x)=8x^2−26x+21.   where the slope of the tangent line is 0. The​…

A: Given : f(x) = 8x^2-26x+21 Find: All points where The slope tangent line is zero. We know tha slope…

Q: 3. For which function is the average rate of change over the interval 1 < x < 5 greater than the…

A: To find- For which function is the average rate of change over the interval 1 &lt; x &lt; 5 greater…

Q: Consider the function f(x) = 2x³ – 3æ² – 72x + 7 on the interval [ – 5, 10]. Find the average or…

A: The average or mean slope of the function f(x) on an interval a,b is defined as f(b)-f(a)b-a. If…

Q: Consider the function f(x) = 3x³ 5x on the interval | – 2, 2]. Find the average or mean slope of the…

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Q: Find f′(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

A: Given a function 'f' of x and find its first derivative . And also find at x=1 tengent line equation…

Q: Given f(x) = x² + 7x, find the average rate of change of f(x) on the interval [ – 1, –1+ h]. Your…

A: Given,          fx=x2+7x on the interval -1,-1+hWe know that,           The average rate of change…

Q: Use the second derivative test to find the relative extrema of the following function. Make sure to…

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

Q: Find the rate of change of the function at a given value. 1. f(x) = 2x – 3, at x = 5 2. f(x) = 2x² ,…

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Q: A note card company has found that the marginal cost per card of producing x note cards is given by…

A: Answer

Q: Use the first and second derivative tests to find the critical points, local max and local min…

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Q: Find the average rate of change of the function over the given intervals.   ​f(x)=6x3+6​;      a​)…

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Q: Consider the function f(x) = 2x³ - 6x² – 90x + 6 on the interval [ – 5, 9]. Find the average or mean…

A: Mean value theorem

Q: Find the function f given that the slope of the tangent line at any point (x, f(x)) is f'(x) and…

A:

Q: For the function f(x) = (3x^3) - (2x) on the interval [-2,2]. What is the average or mean slope of…

A: Obtain the slope of the function on the interval as follows.The given function is f(x) = 3x3 – 2x…

Q: Consider the function f(x) = 10/x + 9 on the interval [1, 7). Find the average or mean slope of the…

A: average slope of a function which is continuous and differentiable between given interval is…

Q: Find the average rate of change of the function over the given intervals.   ​f(x)=7x3+7​;      a​)…

A:

Q: b. Based on the graph of f(x), will the slope of the normal line drawn to the graph of f at x=4 be…

A: Given: The function is fx=2x-3cosx. To show: f'x=1+3xsinxx Differentiate with respect to x:…

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

A:

Q: Consider the function f(x) = 2x³ – 9x² slope of the function on this interval. 108x + 4 on the…

A: Solve using mean value theorem

Q: For the function, find all critical numbers and then use the second-derivative test to determine…

A:

Q: Find the slope of the function f (x) = x 3 + 3x 2 + 3x + 1 at x = 0 1 0 3

A:

Q: Consider the function f(x) = 2/I+3 on the interval 4, 7. Find the average or mean slope of the…

A: Given problem is :

Q: Consider the function f(x) = 2x – 6x² – 48x + 1 on the interval [– 6, 8]. Find the average or mean…

A:

Q: Find the average rate of change of the function f(x)=-2x^2-1x+6, from x=-2 to x=0. Find the average…

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Q: find the average rate of change f(x)=x2+6x from x1=3 to x2=4

A: Given, f(x)=x2+6x x1=3 to x2=4

Q: Find the Average rate of change of the function f(x)=x² – 3.x- 2 on [-2, 4]

A:

Q: Consider the function f(x)=2x^3-9x^2-60x+2 on the interval [-6,8]. Find the average or mean slope of…

A: Given - f(x) = 2x3 - 9x2 - 60x + 2 ................... (1)  Interval =  [-6, 8] f(-6) =…

Q: Consider the function f(x)=2√(x)+3 on the interval [4,5]. Find the average or mean slope of the…

A: The mean slope is given by: f(5)-f(4)5-4=f(5)-f(4)1=f(5)-f(4)

Q: Find the average rate of change of f(x) = 4x² – 7 on the interval [1, 6]. Your answer will be an…

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Q: Consider the function f(x) = 2x interval - 2, 2|. Find the average or mean slope of the function on…

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Q: Find the average rate of change of the function f(x) 2x2 2x- 2, on the interval x E [2,4]. Average…

A: The average rate of change between two input values is the total change of the function values…

Q: Find the average rate of change of the function over the given intervals. ​f(x)=4x3+4​      a​)…

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Q: Find the average rate of change of the function on the interval specified. g(x) = 9x3 − 3  on  [−3,…

A: I have stated the used formula in the solution.

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

A: Recall: Average Rate of Change of a Function :        Ax=f(b)-f(a)b-a; where , f(a) and f(b) are the…

Q: Consider the function f(x)= 6/ +2 on the interval 1, 6). Find the average or mean slope of the…

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Q: 2x2 Using the second derivative test for critical points of the function y = –x' 3 16x, which of the…

A: We have to find out

Q: For the function, find all critical numbers and then use the second-derivative test to determine…

A: Solve by derivative

Q: 2. Estimate the slope of ffx) at the point: a) where x = 3 b) where x = 2 f(x) 4 2 1 2 3 4 5 6 3. 1.

A:

Q: For the function f(x) = 1/x on the interval [5,8]. What is the average or mean slope of this…

A: Given the function is f(x)=1/x.