Find the point on the line y = x that is closest to the point (5, 7). [Hint: Express the distance d from the point to the line as a function of x, and then find the minimur ..... The point is (.).

Q: Calculate the approximation for the given functionand interval:                    M4, f (x) =√x,…

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Q: For the function y = (x − 2) In x, what are the two x intercepts, and between the two intercepts, is…

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Q: Find the distance between the two values of x at which the function is discontinuous. x²- 3x + 2 2.…

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Q: Determine equations of all lines tangent to the graph of f(t) = t° /3+2t² +4t that have slopes of 1.

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

A: First calculate f(x) then use (9,6) to find the constant in f(x). Then find f(5).

Q: Suppose that f is a function given as f(x)=x3+bx2+cx−4 Find the exact values of b and c if we know…

A: Given: fx=x3+bx2+cx-4   and tangent line y=36x+68

Q: At which of the labeled points does f' (x) = 1? B

A: The graph of the function is given by To evaluate : The point at which f'(x) = 1

Q: From the text, the average rate of change of the function f(x) = 8x + 6x over the interval x = 1 to…

A: Given function, f(x)=8x2+6x  interval x=1 to x=2

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: The following Ilinear plot is derived from a function of the form y= ae", where a and b %3D are…

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Q: There is no point on the graph of f(x) = 3x2 4 at which the tangent line is y = 12x- 2. Select one:…

A: We have to consider gi condition is true or false

Q: determine the intervals on which the function is concave up or down and find the points of…

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Q: The graph of f(x) and a line tangent to the curve at x = 4 are shown. If g(x) = f(x), evaluate…

A: Given graph is as follows where the red graph shows f(x)  and a line tangent to the curve at x=4.…

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: 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: tanggent

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Q: Find the area of a triangle bounded by the y axis, the line f(x) = 10 T, and the line perpendicular…

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

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

A: The function is given as fx=kx......(1) The line is given as y=x+4......(2)

Q: For the function f(x) = 4x² + 2, the slope of the tangent line at x = 3 is a m = 32 b m = 4 m = 8 d…

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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: For use after sson 6.3 Use the graph or the table to write a linear function that relates y to x. 2.…

A: So for finding equation of line we are going to use two points formula to calculate equation so I'm…

Q: e. Find the point(s) on the graph of f(x)= 5x³(4x² – 60) that have horizontal tangent lines. |

A: Any function have horizontal tangent line at points where derivative is zero

Q: Given S= -10T^2+4. Is S a function of T? Explain your choice using the definition of a function.

A: Given,    S= 10T² + 4   Yes, here S is function of T.  Thus, S = f(T) = 10T² + 4

Q: Please

A: For concave downward, f''(x) < 0 f(x) = (1-1/x)2 = 1 - 2/x + 1/x2 f'(x) =2/x2 - 2/x3 f''(x) =…

Q: Sketch the level curves of the function f(x, y) = y – ? | for c = 1. 4 -6 -5 -4 -3 -2 -2 -4 -7 Clear…

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Q: Find the exact lenght of the curve. when 0 is less x and x is less than or equal to 1 y=2+2x3/2

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Q: determine the intervals on which the function is concave up or down and find the points of…

A: That is, either function changes from concave up to concave down or vice versa.

Q: 5. Determine the area of the largest triangle that can be formed in the first quadrant by the…

A: The area is found by making a function of area into a variable and finding the values at which…

Q: The area of a disk as a function of radius is given by A = πr². How close must r be to 2.0 cm to…

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Q: Find the y-intercept of the line tangent to the graph of f(x) = 4/æ at x = 9. O 4 Answer not listed…

A: Slope of tangent is obtained by differentiating the function f(x).

Q: Calculate the approximation for the given function and interval.                         M6, f (x) =…

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Q: Find k such that the line is tangent to the graph of the function. Function Line f(x) = kVx y = 4x +…

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Q: f(x) = + 3, X with 0 < x< 3

A: The length(arc-length) of the function is given by: L=∫ab1+(f'(x))2dx

Q: Suppose you have the function f(x) = 3x2 + 4x + 2. %D - A) What is the exact value of the slope of…

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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: 2 The linear approximation for the function f(x) = be used to estimate f(0.01). Which of the…

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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:    f'(x)=3(2x−9)2,  5,32

Q: Find the slope of the tangent line to the graph of the given function f (x) = 4x³ at the point (2,…

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Q: For the graph of f(x) = x-7x² -6x +5, find the value(s) of x for which the tangent to the curve is…

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

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Q: Find the slope of the line that is tangent to the graph of f (x) 2a-3 at P(3/2, 0) О -3/4 O 2 O (E)…

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Q: Fim the Points on the JraPh Of the function that given Poin. asxe Closest to the

A: We use second derivative test to find out point where distance minimum

Q: f(x) = + 2x' with 1 < x< 2

A: Given: fx=x36+12x with 1≤x≤2

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

A: Given, function y=fx=kx and line  y = x + 4

Q: Find the x-coordinate on the graph of f (x) = x3 - 12 x where the tangent is horizontal. (A) 1, - 2…

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Q: Consider the point (x,y) on the graph of the line 6x+4y=7. Let L be the distance from the point…

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Q: Find the slope of the line that is tangent to the graph of f(x)=3x²-2 at P(-3, 25). O -3/25 O 27 O…

A: As per the company's guidelines, we are supposed to solve the first question for you, kindly repost…

Q: Sketch the level curve of the function g(x, y) = x + y? for c 36. 4- -10 -9 -8 -7 -6 -5 -4 -3 -2 -…

A: Level curve