Consider the function defined by f(r) = re + xe¯ + 4: (1) study f and draw its graph, (2) determine the number and the sign of the solutions of the equation f(x) = 0.

Q: At what value of x does the function f(x) =x-2 x change from decreasing to increasing?

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Q: This function has: 1) A y intercept at the point 2) x intercepts at the point(s)

A: Given,  fx=2x2+11x+123x2+10x+3 The x-intercept, y-intercept, and vertical asymptotes are to be…

Q: The domain of the function ,y) = In[x* +y² – 1) is:?

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Q: a) Find the points on the graph of f(x) = 2x- 3r²- 12x + 8 where the tangent is 3. horizontal.

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Q: Find the absolute maximum value of the function f(x) = (x - *).

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Q: Sketch the graph of the function f(x)=-x2 +4x-1. Find the equation of the line that is tangent to…

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Q: (b) Determine the domains and range of this function: y = v1 -x-

A: The given function is y=1-x2 the domain of the function is -1≤x≤1 In the interval notation the…

Q: If f is a function defined by the equation y = f1x2, then x iscalled the variable, and y is…

A: Given: If f is a function defined by the equation y = f(x), then x is called the _________ variable,…

Q: Find the slope of the secant line between x=−2 and x=3 on the graph of the function f(x)=−2x2 −5x+1.

A: The point on the graph when x =-2 is given by plugging x=-2 in the function:Hence, the point on the…

Q: A3) Find the equation of the line tangent to the graph of f(x) = 4x + 3r² – 6x – 4 at x = -3.

A: f(x)=4x3+3x2-6x-4 at x=3,

Q: Find an equation for the line tangent to the graph of f(x) = -6xe" at the point (a, f(a)) for a = 2.

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Q: A3) Find the equation of the line tangent to the graph of f(x) = 4x° + 4x² – 3x – 3 at x = -4.

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Q: (B) Use the second derivative test to find the maxima and minima for f(2) = 22 - 15x + 1. 3 %3D

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Q: find and classify the stationary points of the function f(x)=x^3-2x^2+2

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Q: Find the slope of the secant line between x = -1 and x = 2 on the graph of the function f(x) = -2x +…

A: The given function is fx=-2x3+3. Compute the slope of as follows.

Q: Find the graph of the function f(x) = [x] + [x/2] from R to R.

A: Given function is fx=x+x2. Definition: Floor function is the greatest integer that is less than or…

Q: The slope of the line tangent to the graph of f(x) = 15 – 3a2 at the point z = -8 %3D 48 96 O 12 O…

A: Solution is given below : Answer: 48

Q: Consider the implicit relation yx +1= 7y. In the box below, solve the equation for y as a function…

A: In this question, we have to separate y in terms of x.  i.e. y=f(x)

Q: Determine the equation of the vertical trace of the function g(x,y)=-x^2-y^2+2x+4y-1 corresponding…

A: To find equation of vertical trace we need to substitute value of variable in the given equation of…

Q: with equation -x+3, x -1 f(x) = %3D What is the behavior of f(x) as x gets closer and closer to -1…

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Q: Find the point at which the line f(x) intersects the line g(x) = 2x + 5 = – 2x + 1 -

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Q: The point of the given function at (2, -7) is found to be y = x3 – 2x2 – 4x + 1

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Q: 2. Use the graph of the function f(x) to estimate where (a) f'(x)= 0, y f(x) (b) f'(x) 0.

A: (a) f'(x) =0   => the slope is zero, it means when the graph is parallel to x-axis  i.e. at…

Q: 7) Find the difference auotient. f(x+h)-f(x) for the function, f(x) = x² + 3x - 4.

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Q: Use the graph of the function f to find approximations of the given values. y 4-

A: To find the values of f at x= a,  we imagine the vertical line x=a and where the vertical line…

Q: 7. Determine the equation of the function with zeros at ±1 and - 2, and a y-intercept of-6. Then…

A: We have to find function

Q: 2 For what values of x does the graph of f(x) = 2x° + 3x – 180x – 1 have a horizontal tangent line?

A: First we find the derivative of f(x), the slope of f(x) for horizontal tangent is 0 and the…

Q: Find the point at which the line f(x) = – x – 2 intersects the line g(x) = 3x + 6

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Q: Let f(x) = x2. Give an equation of the line that intersects the graph of f(x) at x = 0 and x = V2.

A: Given data:     The given function is: f(x)=x2. The first value of x is: x1=0. The second value of x…

Q: For what values of x does the graph of f(x) = x3 + 3x 2 + x + 3 have a horizontal tangent?

A: the given function is: fx=x3+3x2+x+3 we have to determine for what values of x does the graph of…

Q: 16. Find the range of the function y = 1+ x2

A: Range: The range of the function is the set of all values of the dependent variable y corresponding…

Q: Graph the function f(x)=−4x2f(x)=-4x2 and draw the tangent lines to the graph at points whose…

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Q: Consider the function f(x)=x^2+2x+2  what is the equation of the line of symmetry of f?

A: To find equation of line of symmetry of function fx=x2+2x+2

Q: Find the point at which the line f(x) = 2x – 3 intersects the line g(x) = 5x – 6. %3D

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Q: In certain conditions, the atmospheric pressure (p) in the height (h) is given by p=29e-0.000034h.…

A: It is given that the atmospheric pressure in the height is given by the function…

Q: The slope of the line tangent to the graph of f(x) = 18 – 5x² at the point x = -8 O 20 O 10 O 160 O…

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Q: dont understand the fourth and fifth row of equation of gh(x) and why the function is invalid?

A: Solution

Q: Find the slope of the secant line between x=−3 and x=4 on the graph of the function f(x)=3x2−x+2.

A: we will find slope of secant line by two point slope formula

Q: Find the relative extrema of the function and classify each as a maximum or minimum. (Use either the…

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Q: Consider the function f(x) = i + x². How does this function essentially behave for large positive…

A: The Given Function f(x) contains rational function x/(x2+1) and polynomial function function…

Q: Find and classify the extreme point of the function f(x, y) 3y2x + x³ - 3y3 - 3x? + 2.

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Q: Find the slope of the secant line between x=3 and x=5 on the graph of the function f(x)=−2x^2+2x+5.

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Q: Find an equation of the line tangent to the graph of f(x) at the point (5,9): f(x) = e-3x-1o + 8

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Q: The graph of f (x) = ax+b x²+3x-8 has horizontal tangent at (2, -1). Determine the values of a and…

A: Given query is to find the value of a and b.

Q: Write the equation of the line tangent to the graph of f (x) = -3x² + 5x + 1 at x = 1 and use it to…

A: We have to find the tangent line equation and also we have to approximate f(1.2).

Q: 3 The graph of f(x) = 2x° + 15x² – 84x + 24 has two horizontal tangents. One occurs at a negative…

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Q: Find a formula for the quadratic function whose y-intercept of y = 3 and x-intercepts at x = 1,…

A: Given: y-intercept y=3 x-intercept at x=1,4

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.