a.) What do you notice about the y-values as x- values increases? b.) What functions have you seen that have this general shape?

Q: Given that the graph of f(x) passes through the point (6, 9) and that the slope of its tangent line…

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Q: Determine the missing coordinates of the points on the graph of the function

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Q: Let y = e? Then the x Coordinates of the inflection point(s) of this function is (are)

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Q: The slope of the tangent line to the graph of the function y = 3/I – 6 at (36, 12) is, O -0.67 O…

A: Given function is y=3x-6. We have to find the slope of function at point 36, 12   Slope=dydx…

Q: Do the graphs of the functionshave any horizontaltangent lines in the interval 0≤ x≤ 2p? If so,…

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Q: , Find the equation ofthe line thet Is tangent to graph of the giren functlon at the Point CC, fC)…

A: First you will find the slope of the tangent by using the fact that the derivative of the function…

Q: 4 The function f(x,y) = corresponds to x² + y? plot [ Select ] level curve [ Select] >

A: Here, the given function is: f(x,y)=4x2+y2

Q: For what values of x does the graph of f have a horizontal tangent? f(x) = x +2sin(x)

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Q: 1+x? b. y = 2 1-х*

A: The solution are next step

Q: Use the vertical line test to identify graphs in which y is a function of x.

A: Vertical line test: If every vertical line cuts the graph only once then the graph will be a…

Q: The heights on the graph of f'(x) correspond to the slopes of the lines tangent to the graph of f.…

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Q: A hypothetical function representing the concentration of a drug in patient's bloodstream over time…

A: Given c(x) = 5xx2+1 x c(x) 0 5(0)02+1 = 0 1 5(1)12+1 = 52 2 5(2)22+1 = 2 3 5(3)32+1 = 32…

Q: For what values of does the graph of f(x) = x +2Sinxhave a horizontal tangent?

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Q: Sketch the level curves of the function f(x, y) = y + x? for c = 3. 7- 5- 4- -6 -5 -4 -3 3 4 5 6 -2…

A: Solution ) f(x,y) = y + x2  f(x , y ) = c  y + x2  = c  y + x2 = 3  y = -x2 + 3 To find the vertex…

Q: Consider the graph of f (x) = 16 – x². f(x) P Find the coordinates of the point P in the graph at…

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Q: (a) How is the length of a curve defined?(b) Write an expression for the length of a smooth…

A: Definition : The length of a curve is defined as the limit of sum of lengths of line segments when…

Q: Find the points of inflection and discuss the concavity of the graph of the function.

A: Given: f(x)=tanx4, (0,2π)

Q: Do the graphs of the functionshave any horizontaltangent lines in the interval 0≤ x≤ 2p? If so,…

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Q: What is the range of the secant function?

A: For the secant function: y=secx Range is: y≤-1,or,y≥1 Or in interval notation: secx∈ (-∞,-1]∪[1,∞)

Q: Find the point of inflection and discuss the concavity of the graph of the function. f(x) = sin ,…

A: Inflections points are those points at which second derivative is 0.

Q: The graph of a function is shown together with the tangent line at a point P. y 10 9 8 6. 5 4 2. 3.

A: Tangent line: - A tangent line is a line that touches a curve at only one place locally. The…

Q: the function y=f(x) is shown below. how many inflection points does this function have on the…

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Q: Consider the function f(x) = x In x. Out of all the many tangent lines of f (x), determine the one…

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Q: Consider the function f(x) = e2x. Out of all the many tangent lines of f (x), determine the one that…

A: Topic;- application of derivatives

Q: Does the graph ofhave a vertical tangent at the origin? Give reasons for your answer.

A: Given: f(x)=-1,x<00,x=01,x>0

Q: . What effect does a vertical stretch or compression have on the y values of a function? What effect…

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Q: What is the domain and the range of y = sec x?

A: y=sec x or y=1cos x∴ sec x is undefined at cos x=0cos nπ+π2=0   ∴ x≠ nπ+π2 Thus, the domain of the…

Q: 1) . (a) At what values of x does the graph of f in Fig. 1 have a horizontal tangent line? (b) At…

A: (a) The function f(x) has horizontal tangent at x=1, x=3 and x=4. It occurs at point where function…

Q: Sketch the level curves when z = 5 and z = 8 for the function z = z + y? + 4. Hence, sketch the 3D…

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Q: Is the function y=sec x always defined? Why or why not?

A: y=secx

Q: Does the graph ofhave a tangent at the origin? Give reasons for your answer.

A: Given function is fx=x2sin1x , x≠00,             x=0

Q: 41. Aroller coaster has the shape of the graph in Figure 19. Show that when the roller coaster…

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Q: Is the following function a proper distance function? Why? Explain your answer. Measure the distance…

A: By the definition of distance function, distance between any element is non-negative. The given…

Q: At what point(s) on the curve x

A: Given that : The curves are x = 3t2 + 9 and y = t3 - 2. Slope of the tangent line is 12 .

Q: Find the equation of the tangent line to the graph of the function f (2) = (22 +7) (x– 2) at the…

A: Given curve f(x)=(x2+7)(x-2) ⇒f(x)=x3-2x2+7x-14

Q: Given that the graph of f(x) passes through the point (5, 8) and that the slope of its tangent line…

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Q: Express the hupotenuse of h of a night triangle with an area of 25 m a function of its peri meter P.…

A: This question is based on Triangle.

Q: The tangent, cotangent, and cosecant functions are ________, so the graphs of these functionshave…

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Q: What effect does a horizontal stretch or compression have on the y values of a function? W effect on…

A: Horizontal Stretches and Compressions When we multiply a function’s input by a positive constant, we…

Q: Graph the function f(x) = are -2 , 0, and 1. 3x and draw the tangent lines to the graph at points…

A: Given: f(x)=-3x2 y=-3x2  x=-2,0,1x=-2 ⇒y=-3(-2)2=-12⇒(-2,-12)y=-3(0)=0⇒(0,0)y=-3(1)2=-3⇒(1,-3)

Q: Examine this figure showing the graph of y = f() y = f(x) (10, 4) Tangent line (4, 2) and estimate…

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Q: What is the range of y = sec(x)?

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Q: Explain with drawing the effect of increasing of each value of (A,B and C) on graph of…

A: The given function is: y=A+B sin (Cx)

Q: At what values of x, if any, is the function shown below not differentiable? 5+

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Q: Estimate the value of the function, whose graph is shown in red, at x = 2.2 if the tangent line to…

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Q: Find the exact value of fo f(x) dz for the function f(x) graphed below.

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Q: ind the equation of the osculating circle at x=2 for y= 1/4x^2-x. Draw the circle

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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: