Consider the function f(x) = 3x³ Find the slope of the secant line on this interval. 6x on the interval [ – 3, 3]. Find the value(s) for c that satisfy the Mean Value Theorem in the open interval ( – 3, 3). - c =

Q: Find all points (x.y) where f(x.y) has a possible relative maximum or minimum. Then use the second…

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Q: Use the First Derivative Test to find the local maximum and minimum values of the fu M(t) = 4t3 +…

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Q: For #2 and # 3 use the first derivative test to find the extrema point(s). 8. #2) f(x) = x* – 2x³ +…

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Q: Find the mean value of the function y = 4cos x on the interval 0,

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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: Use the derivative of the function shown below to determine the open intervals in which the function…

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Q: ) determine the rate of increase of the infection by sovid19 outhreak size A with respect to p the…

A: Answer

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

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Q: Let f(x) = In(x* + 1). Find the slope of the secant line thru x = 1 and x = 1.01 .

A: We have to find

Q: Find the average fave of the function on the given interval. f(x)= 3x^2+4x, [-1,4]

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Q: For a-b: consider f(x)=x* +x-4 on the interval [-1,2]. a. Find the slope of the line secant line…

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Q: Find the critical points of the following function. Use the Second Derivative test to determine (if…

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Q: Find the interval of x-values on which the curve is concave up and concave down , then sketch the…

A: (1) Given a function, fx=x33+x2-3x

Q: f(x,y) = 2y3–3y² – 12y+2x2 – 4x+2.

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Q: Find f(x) if f(2) - 2x 3 and the tangent line at x has slope (x – 1)e* %3D f(x) =

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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: 4) Find all values in the interval [-27,27]at which the graph of f has a horizontal tangent line.…

A: topic- functions and derivatives

Q: A rectangular field is to have an area of 900 sq . m. This is to be enclosed and divided into three…

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Q: For what value(s) of x does the function f(x)= 4x3-x2-2x+5 have a horizontal tangent line?  a.) x=…

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Q: (A) Find the absolute maxima and minima for ,3 Y = x + 5 over [-V2, v2). (B) Use the second…

A: y = x33-x+5y' = 3x23-1y' = x2 -1x2-1 = 0x2 = 1x = ±1

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

A: Given query is to find the function.

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

A: The objective is to find the mean value of the function and find the values of c for which f'(c) is…

Q: The function f is defined by f (x) = - What point(s) (x, y) x+4 on the graph of f have the property…

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Q: 1.Use the second sufficient condition for an inflection point (the third derivative test) to find…

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Q: Consider the graph of the function f(x)=x^2-x-12 and perform the following tasks.  a) Find the…

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Q: Let f(x) = 2x² 11a + 4 - The slope of the tangent line to the graph of f(x) at the point (2, 10) is…

A: This is a problem related to derivative of the function. Please follow the procedure given below.

Q: Find the value(s) of "c" that satisfy the conclusion of the Mean Value Theorem for the derivative of…

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Q: Find f(x) if f(5) = 0 and the tangent line at (x, f(x)) has slope x/x2+7. f(x) =

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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: Suppose the linear approximation for a function f(x) at a = 3 is given by the tangent line y -2x +…

A: The given functions are

Q: Find the points guaranteed by the Mean Value Theorem and sketch the associated graph. The slope of…

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Q: b. Use the Second Derivative Test to find all local minima and local maxima for g(x).

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Q: Find the critical point of the function. Then use the second derivative test to classify the nature…

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Q: Let f(x) =4x divided by x -3. Find the slope of the secant lines on the graph of F through P(5, 10)…

A: f(x)=4x/(x-3) P(5,10) and Q (6, a)  (say) a= f(6)= 24/3 =8  Q(6,8) is

Q: Let f(x) = 9 – x² The slope of the tangent line to the graph of f(x) at the point (-3,0) is The…

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Q: Let f(x) = In(x"+1) Find the slope of the secant line thru x = 1 and x = 1.01.

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Q: Consider the function f(x) = 9x² +3. Its tangent line at x = 6 goes through the points (1, y1) and…

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Q: Let f(x) = 25 x The slope of the tangent line to the graph of f(x) at the point (–6, – 25) is The…

A: All the answers are given below

Q: Consider f (z) =r - 3z +1 on [-4, 2]. Find the average or mean slope of the function on the…

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Q: Consider the function f(x) = 9x + 3. Its tangent line at x = 6 goes through the points (1, y1) and…

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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: Find the values of x for which f (defined below) has a horizontal tangent line f(x)=(1/3)x3…

A: To Find the values of x for which f(x) has a horizontal tangent line f(x)=(1/3)x3 -(1/2)x2 -6x+7…

Q: find all the values of x for which f(x) will have a horizontal tangent line f(x)=(x-4)/(x^2-7)

A: Given equation f(x) For horizontal tangent line the slope f'(x)=0

Q: The functionf(x) is Find the first derivative in fa Set up a number line with t increasing,…

A: The given function is fx=3x5-5x4. Find the first derivative of the function by the power rule of…

Q: Graph the function f(x) = - 3x - 3 on [0, 3] and find its average value over the interval. Choose…

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Q: 3 Given the function f(x) = 2a2 – a + 2, find the points where the tangent line has slope – 4| 2 а)…

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Q: Find the average rate of change of f (x) = 3x² – 4 over the following intervals. a) [0,3] b) [-4, 1]…

A: Average rate of change = f(b) -f(a)b-af(x) = 3x2-4a) (0,3) Average rate of change = f(3) -f(0)3-0…

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.

Q: Using the definition, find the derivative of f(z) = 3 zª-6 z² at point z= 0

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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: