Two vehicles start out traveling side by side along a straight road. T owing graph, are given by s = f(t) and s = g (t) , where s is meas onds.

Q: For what value of x does the graph of y = eš (4x – 5)° have a horizontal tangent line? -

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Q: To shift the graph of f(z) = clog, (dz + g) - a+ change the parameter g. vertically down diagonally…

A: Given query is to find the effect of parameter g on the graph.

Q: C. If h(x) = [f(x)]² + g(x),what is the equation of the line tangent to the graph of h at x = -2?…

A: First we will find derivative of h(x) at x=(-2) that gives the slope of the required tangent.

Q: If f(2)=−7 and f′(2)=3, then the equation of the tangent to the curve y=f(x) at x=2 is

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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: Use the following graph to identify the points on the interval [a, b] at which local and absolute…

A: Local maximum values are at x=p and x=r     Local minimum values are at x=q and x=s.

Q: The graph of ax + b f(x) = (æ – 1)² has a horizontal tangent line at (–3, –). Find a and b.

A: For horizontal tangent line at a point derivative of the given curve is zero , just used it and…

Q: The graph of a function f is given below. JW y = f(x) X

A: from left graph of f(X) is increasing , f'(x) > 0  after that slope of line is steeper ,…

Q: Assume y = 3 · 5* is the equation for the blue line shown in the graph below, and that the black…

A: The equation of curve is:  y=3·5x

Q: For what value(s) of x does the graph of f(x) = 6x³ + 9x² – 216x %3D e a horizontal tangent?

A: To find the values of x does the graph of fx=6x3+9x2-216x have a horizontal tangent.

Q: (i) Find the values of k for which y= kx + 2 is a tangent to the curve y= 4x2+ 2x + 3.

A: If y = kx +2 is tangent to the curve y=4x2+2x+3, then the point of intersection of the line and the…

Q: When f"(x) is negative, the curve of y =f(x) is concave A downward B upward c) to the left D to the…

A: when f''(x) < 0,than than curve of f(x) is concave downward option (A) downward

Q: Use the graph of Jy=f(x) to answer the following.

A: The function, y=f(x) is graphed in the given figure.

Q: 2. Given the function, find the slope of the line tangent to the curve: f(x) = v5x + 2 at the point…

A: We have to find the slope of the line tangent to the curve: f(x)=5x+2 at the point P(1,2) for the…

Q: f(x) = x², with 0 < x < 6

A: Length of the curve y=f(x)  from   x=a to x=b   is give by  L=∫ab1+dydx2 dx

Q: Let f(x) = 4x + 7 – 17e². Then the equation of the tangent line to the graph of f (0, -10) is given…

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Q: sketch the graph of the given function on the interval t ≥ 0.  2.g(t)=f(t−π)uπ(t),where f(t)=t2

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Q: Q2/Find the length of the curve T = sino + cose between -s0s

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Q: Suppose C is the graph of y = f(x) for a < x < b. Compute x dy + y dx in terms of f.

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

Q: Let f(x) = 10x + 12 - 9e. Then the equation of the tangent line to the graph of f(x) at the point…

A: given f(x)=10x+12-9ex

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = 11 e*+…

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Q: Q6. Find the equation of the tangent line to the graph f(x)=2xsinx at x=7

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Q: Suppose that f is a function given as f(x) = x° + bx? + cx – 2. Find the exact values of b and c if…

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Q: Find an equation of the tangent line to the graph of f at the given point. f(t)= (t -…

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Q: Let f(x) = 6x + 2 – 7e*. Then the equation of the tangent line to the graph of f(x) at the point (0,…

A: Here we find the tangent equation then we find the value of m and b.

Q: |The graph of ах + b f(x) = (т — 1)(» — 4) has a horizontal tangent line at (2, –1). Find a and b.

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Q: Determine the length of the curve obtained from the graph of the function e +e=* f(r) = from r = -1…

A: We will find the length of the curve from the graph of the given function as shown below

Q: Find an equation of the tangent line to the graph of f at the given point. f(s) = (s – 3)(s² – 4),…

A: givenf(s)=s3-3s2-4s+12at(-2,0)

Q: Given that f(-8) = 2 and f '(-8)  = 3, find an equation for the tangent line to the graph of y =…

A: Given that f-8=2

Q: If f'(4)= 6 and g'(4)=3, then the slope of the tangent line to the graph of y=2f(x)-5g(x) at x=4 is…

A:

Q: 18 f(t) = t + 2 If an object is moving along a path that can be described as

A: ft=18t+2 Differentiate the above function with respect to t. f't=ddt18t+2=-18t+22

Q: 3 f(x) = x2, with 0 < x < 1

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Q: For what value(s) of x does the graph of 1 f(x) = – x² +3 have a .2 - horizontal tangent?

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Q: Let f(x) = 8x + 10 – 3e². Then the equation of the tangent line to the graph of f(x) at the point…

A: The given function is: f(x)=8x+10-3ex

Q: The graph of y = fx) and the tangent to the curve at x = 1 is shown below. ..... 5 3 y - f(x) -1 0.

A: Consider the given figure.

Q: What is the slope of the tangent line that touches the graph of In y + e2¤¬1 = 3y – 4x at the point…

A: Given query is to find the slope of the tangent.

Q: At which point(s) does the graph of  y= e((x3-2x2+3x)/(x)) have a horizontal tangent line?

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Q: Consider an F-curve with d f = (2, 14). Identify the degrees of freedom for the denominator.

A: The degree of freedom for F ratio is (k-1, N-k), where k is the number of treatment conditions and N…

Q: ) Given that f(8) = 5 and f'(8) = 7 , find an equation for the tangent line to the graph of y = f(x)…

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Q: suppose the line tangent to a graph of f at x = 4 is y = 3x+2 and suppose y = 5x -3 is the line…

A: Given information:The line tangent to a graph of f at x = 4 is y = 3x+2 and suppose y = 5x -3 is the…

Q: Find an equation for the line tangent to the graph of at the point (a, f(a)) for a = = 2. y = f(x) =…

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Q: please help

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Q: Choose the correct graph of y = sin x, -"sxS T: 1 -37 21 -1 -2

A: The given function is: y=sin x ;                 -3π2≤x≤π

Q: Does the graph of S0, x< 0 U(x) = 1, x2 0 have a vertical tangent line at the point (0, 1)? your…

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Q: Find an equation of the tangent line to the graph of y = B(x) at x = 24 if B(24) = 0 and B'(24) = -…

A: Given,         y=Bx at x=24 if B24=0 and B'24=-14.

Q: Sketch the graph of h(t) = |t| + |t + 1|

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Q: Based on the graph dete original function h(x) a) interval(s) where h(.

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.