Find the interval(s) on which the function is negative. y = x2 - 6x - 16 I. (- 00 · 2) II. (- , 3) III. (-2, 8) IV. (8, O Ill only O Il only O lonly 8. 8.

Q: The point on the curve y = 2-x nearest to (3,2) is (1,1) (0,2)

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Q: Find the slope of the secant line to the function f(x)=x3 when x=1 and x=2.

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Q: For the​ function, find the​ point(s) on the graph at which the tangent line has slope 5.…

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Q: Find the points of intersection of the line y = 5 x with the curve y = 3 x + x^2

A: In order to find the point of intersection of given line line and curve , we must find values where…

Q: The line whose slope is -3 is tangent to the curve y = x² + 3x + 2 at the point 0 (-3, 2) 0 (3, 2) 0…

A: We will solve the problem.

Q: find the slope of the tangent line to the graph of the following function at the given point fx…

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Q: -Find the range of the function y = 2 - sin3x

A: Introduction :

Q: An Object moved in horizontal coordinate line according to f(x) = x^3 - 6x^2 , where f is directed…

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Q: Find the slope and equation of the line tangent to f (x) = x² – 4 at the point (3, 5).

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Q: Find the direction in which the function is increasing most rapidly at the point Po. f(x.y) = xy? -…

A: Given,     f(x,y)=xy2-yx2

Q: Determine the slope of the line tangent to y = √² - 3 at x = 2 In case you need help inputting your…

A: The objective of the question is determine the slope of the tangent to the given function.

Q: For the function y = (9x2 - 27)/x3 , determine the increasing and decreasing intervals, and identify…

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Q: If x + y represents a motorboat’s average velocity with the current, in miles per hour, its distance…

A: We can say Average Velocity=Average DisplacementTotal time=dt so according to the question…

Q: Find an equation for the line tangent to the graph of  f(x)= 2xex at the point (3,f(3)). y=?

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Q: Find an equation of the line tangent to the curve defined by æ° + 2xy + y% = 104 at the point (2,…

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Q: For the function y= 9x^2+8x+4,at the point x=4, find the following (A) the slope of the tangent to…

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Q: find the first and second derivatives

A: Given expression: w=3z7-7z3+21z2

Q: Find the indicated value of the function f(x,y,z)=2x-7y + 4z³ -7. f(6, -5,3) f(6, -5,3)=

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Q: Find an equation of the line that is tangent to the graph of the function f(x)= 2x and parallel to…

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Q: y = 2x' + 5x from the point (-2,-26) to the point (4,148), you'd have to compute f(x)dx

A: Given: y=2x3 +5x Point (-2,26) ,(4,148)

Q: for the function f(x)=11x^3-x, find the slope of secant line at interval [1, 1.01]

A: We have given a function f(x).

Q: F(x) = -7+ x2 INTERUAL-ピ-3 -2. AUERAGE RATE of

A: Given query is to find the rate of change for the given interval.

Q: Find the x-and y-intercepts of the line that is tangent to the curve y = x3 at the point (-2, -8).

A: The equation of tangent line to a curve y = f(x) at a point (a,b) is given by the below equation.

Q: - Find the point of tangency and the equation of the tangent line passing through the point p(-4,-2)…

A: Given: Now, f'(x)=-3-2x. At (-4, -2), slope = -3-2(-4) = 5. So, the equation of the tangent line is…

Q: 3) Calculate the length of the curve interval [-2₁2]. y = x²/2 on the

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Q: Find the slope of a line that is tanget to f(x)= 1/x at the point (2,1/2).

A: Given:

Q: Find the derivative. 1) f(x)= V7,7x A) 7.7)4/5 B) 7.7)-1/56 ,7) D) 2) y = x/10x-8 15x-8 A) 15x B)…

A: 1) Obtain the derivative of f as shown below: f'x=ddxx7+7x5       =15x7+7x-45ddxx7+7x…

Q: What is the equation of the line tangent to the function y = 2³+7x² + 5x - 2 at x = 0? There can be…

A: Application of differentiation

Q: Find the slope of the curve at the point (2,3) * x³ 2x + 1 3/2 1 O 1/2 O 1/4

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Q: Find the length of the curve 9y2=8x3 from x=o to x=12 when y>0

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Q: B. Apply the quotient rule to find the derivative 1. y 4-7x 3. y = 5- 3x

A: From the quotient rule of derivative we get Let,  y=uv where u and v is function of x then dydx=…

Q: Find an equation of the line tangent to the curve defined by æ° + 2xy + y = 104 at the point (2, 2).…

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Q: Find the set on which the curve is concave upward. Answer (in interval notation): 2 y = ₁² R² + ² +…

A: See the details solution in below

Q: Find an equation of the line that is tangent to the grapt Function Line 4x-y+2 = 0

A: Since, we have been given up the function:-f(x)=2x2 -(i)Differentiating equation-(i), with respect…

Q: The slope of the curve y^2-xy-3x=1 at the point (0,-1)

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Q: Find the equation of the line tangent to the graph of the function at the indicated point f(x) = x?…

A: Given curve :

Q: What are the coordinates of the points in the graph of y? - - x2 + 6x – 13 = 0 in which the tangent…

A: Note that the slope of a horizontal line is zero. Also the slope of a tangent is given by the…

Q: -4 - Find the derivative for the function f(x) = (5x−4+ 3x + 7) (8x−³ − 7x + 10) 5. Do not simplify…

A: Given, f(x)=5x-4+3x+78x-3-7x+105

Q: The line whose slope is 3 is tangent to the curve y=x² + 3x + 2 at the point, O (3,-2) O (-3,2) O…

A: The line whose slope is -3 is tangent to the curve y=x2 +3x+2 at the point. Here slope and line…

Q: Find the length of the curve on the interval 3/2 Y= (10x+ 15) 15

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Q: Find the slope and an equation of the tangent line to th 3 2 3. f(x) = + 8x + 8; (-1, 21 slope 11…

A: Recall: Point-slope intercept form :  y-y1 =m x-x1 where , 'm=dydx' is the slope and x1,y1 are given…

Q: A particle travels along a horizontal line according to the function s(t) = -3t° +t² + 3t – 2 where…

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Q: II. Find the second derivative 1. y= 8x- 12x3 + 6x?-9 2. y = (4x-9)2

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Q: F(x) = L", costdt π/2

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Q: The equation of the tangent line to the curve x2 + y? = 64, at (5,-13) is. 13 (x – 5) + 13 y = y =…

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Q: Find equations of the two tangent lines to the graph of f(x): x2 that pass through the point (-1,…

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Q: Find the first and second derivatives of the function. w=((3+4z)/4z)(4-3z)

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Q: Find the equation of line (L) that passes through the intersection point of che two functions y = v2…

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Q: x +4 3. y = [- (x2+1)7 :3

A: Given that y=x+4x2+13 Simplifying we get y=x+43x2+132