Choose the correct graph of f. Use the graph of f to sketch a graph of f'. OA. OB. В. Ay 10어 Ay' 10 Ay 10- 8- 1985 1990 1985 1990 6- -10 -10 4- Oc. OD. 2- AY 10- Ay 104 0- 1985 1986 1987 1990 1988 1989 190 1990 1985 10-

Q: Two tan gents are drawn to the function f(x) = x2 - 4x %3D + 10 through the point (1, -9). Find the…

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Q: The slope of the tangent line to the graph of the function y = 7V-3 at (9, 18) is

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Q: What must be done to a function’s equation so that its graph is stretched vertically?

A: The graph of a function is stretched vertically.

Q: Match the graph of f, below, with that of its derivative. 3. -3 -2 -1 I 2 3 -3+ 4 ++ -6 -4 -2 4 6 2.…

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Q: find the slope of the tangent line to the graph of f at the given point f(x)=x^2-8x+2 at (2,-10)

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Q: What is the slope of the secant line that passes through the points(a, f(a)) and (b, f(b)) on the…

A: Given: The secant line passes through the points a,fa  and  b,fb. Concept used: The slope of a line…

Q: Consider the functionf (x) = 3x² + x. Select the figure with the tangent line (blue color) at x = 1…

A: The correct figure is figure 2

Q: At what points is the function is continuous y=|2x-1| +4sin(2x)

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Q: The slope of the tangent line to the graph of the function (16, 24) is - O 1.25 O 0.88 O -2.00 | O…

A: Given function -  f(X) = y = 7√x -4

Q: Find the slope of the tangent line that passes through point (1, 2) to the graph 8y³ + x²y O-2/97…

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Q: Determine the point(s) at which the graph of -8x f(x) 2x - 1 has a horizontal tangent.

A: Given that  f(x)=(-8x)/(√(2x-1))  The function has a horizontal tangent  To find the point at which…

Q: Sketch a graph of the function f(x) = 0.5 sin(3x). 4+ 2 -5/6 -27/3 -T/2 -T/3 -Tt/6 T/2 2/3 5/6 -1 -2…

A: Here is the solution

Q: Find an equation of the tangent line to the graph of y = f(x) when x = 2 if f(2) =-6 and f'(2) =5.

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Q: In the given question , find equations of the two tangent lines to the graph of f that pass through…

A: Given function and point is  f(x)=x2,  1, -3

Q: Find the equation of the tangent line to the graph of x4y16=1 at the point (81,1/3) and at the…

A: We use slope point form to equation of tangent line.

Q: For f with derivative as in Figure : (a) Is f (c) a local minimum or maximum? (b) Is f a decreasing…

A: The function has local maxima or minima depending upon the first derivative as, If the sign of first…

Q: The slope of the tangent line to the graph of the function y = 7Vx – 3 at (9, 18) is - O 3 - 2.00 O…

A: Simply take the derivative of the function at that point.

Q: When is a function periodic?

A: A function is periodic if there exists a positive real number M such that, fx+M=fx The smallest…

Q: Sketch a graph of the function f(x) = 2 sin(z) %3D 6+ 5 4 3 -6 -5 -4 -3 -2 -1 -- 6 7 -9 -8 -7 2 3 5…

A: How to solve: make a graph of sin(x) and then transform it one by one:

Q: An even function is symmetric with respect to the________

A: An even function is symmetric with respect to the________

Q: Suppose that f is a function defined as f(x) = – 5x + 3x + ¤ + 3. Find an equation for the tangent…

A: Given function is: fx=-5x3+3x2+x+3 We have to find the equation of the tangent line drawn to the…

Q: Select the graph of a function f that satisfies f' 0 on (-0, -1)U(-1, 0).

A: means f is decreasing for x> - 1   means f(x) is concave up on both sides of x=-1

Q: Sketch a graph of the function f(x) = 3 cos 6 5 4 3 2 1 -8п -7п -бп -5п -4п -3л -2л -π -1 -2 -3 -4…

A: This question is based on graphing a function from its principal function.

Q: Is the cosecant function even, odd, or neither? Is its graph symmetric? With respect to what?

A: A function is "even" when: f(x) = f(−x) for all x A function is "odd" when: −f(x) = f(−x) for all x…

Q: The tangent line to the graph of a function f at the point x =2 has x-intercept 10/3 and y-intercept…

A: Given query is to find f(2) and f'(2)

Q: 5. State the domain and the range of the tangent function.

A: Consider the tangent function Give the domain and range.   Since tan x=sin xcos x therefore, tangent…

Q: Sketch the graph of f. fx) 5 fx) 5 4 3 2 2 1 1 3 4 4 -3 -2 -1 1 3 4 -4 -3 -2 -1 -1 -1 f(x) f(x) 5, 3…

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Q: Suppose that f is a function defined as f(x) = 5x3 + 3x2 + x + 3. Find an equation for the tangent…

A: f(x)=5x3+3x2+x+3Derivative formuladdxxn=n xn-1

Q: Find k such that the line is tangent to the graph of the function.

A: f(x) = k−x²and the given line is y= −8x+5slope of the line = −8Now f'(x) = −2xtherefore,  −2x = −8…

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

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Q: 5.) Assume that the given graph gives the position function of a particle which is moving along a…

A: Consider the given graph showing the position function of a particle which is moving along a…

Q: Select the graph which satisfies all of the given conditions. f' (-3) = f' (1) = 0 Increasing on…

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Q: Suppose the second derivative of a function f is f" (z) 0 (-∞, 1) U (1, 3) U (5,00) ○ (3,5) O (1,3)…

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Q: The graph of f"(x) , the second derivative of f, is shown below. If the point (2, f(2)) is a…

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Q: Suppose f(1) = Let h(x)= arcsin(f(x)). h'(-1) = and f'(1) - 2.

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Q: Find the directions in which the function increases and decreases most rapidly at Po-

A: Given, fx,y,z=4lnxy+lnyz+lnxz, P01,1,1 Direction in which function f increases is given by, u^=∇f∇f,…

Q: Sketch the graph of the function. (Include two full periods.) 2лх y = 4 – sin 3 y y 1 5 9 3 3 3 9 -3…

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Q: Sketch a graph of the function f(x) = – 2 sin (x + 4) +: + 1. 5+ 4 3- -37/2 -5/4 -3/4 -T/2 -TU4 3714…

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Q: Sketch a graph of the function f(x) 2 cos(Tz) +3 -

A: Given Function :

Q: based on what we know a function to be today, what did Euler mean by an analytic expresstion?

A: According to Euler, An analytic expression is an expression formed from operations such as addition,…

Q: Find the equation of the tangent line to the graph of the function f(2)=√1026 +26 at the point…

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Q: The slope of the line tangent to the graph of position as a function of time at t = to

A: The slope of the line tangent is in the form of a difference quotient approach t=t0 is, m=ft-ft0t-t0

Q: Consider the following function. f(x) = x* + 4x3 + 11 (a) Make a sign diagram for the first…

A: We have to find the sign diagram for first derivative,  sign diagram for second derivative,  sketch…

Q: For f with derivative as in Figure 13: Is f(c) a local minimum or maximum? Is f a decreasing…

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Q: Sketch a graph of the function f(x) = - 4 cos 6+ 4 2 -8л -7л -бл -5л -4л -3л -2л -л) 2л Зл 4л 5л бл…

A: We need to draw the graph of

Q: Sketch a graph of f(x) = 3 sin[2 (x – "}+1 for two cycles. -

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Q: Suppose that f is a function defined as f(x) = xª . drawn to the graph of f at x = 1. Use exact…

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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: