Find all points (x, y) on the graph of f(x) = x - 2x² + 5x + 24 with tangent lines parallel to the line 10x- 5y = 3. ..... The point(s) is/are (Type an ordered pair. Use a comma to separate answers as needed.)

Q: Estimate the slope of the tangent line to f(x) = x³ at x=2 by finding the slope of the secant line…

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Q: 2. Let f(æ) = 2e* – 3x² /a, whose graph is given to the right. Sketch in the tangent lines to f(x)…

A: Graphed the tangents using a graphing calculator.

Q: (a) If F(x) = 6x/(2 + x2), find F '(2) and use it to find an equation of the tangent line to the…

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Q: Find all the value(s) of x at which f(x)=(7x^3/3)+3x^2−x+9 has a horizontal tangent line.

A: The values of x at which the given function has a horizontal tangent line can be found by evaluating…

Q: Find all points (x, y) on the graph of f(x) = x - 3x + 8x + 23 with tangent lines parallel to the…

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Q: The product of all the values of x for which the tangent lines to the graph of y= are parallel to…

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Q: Find an equation of the tangent plane to the graph of f(x, y) = at the point (2, 9). y Z =

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Q: Find the equation of the tangent plane to 4 = Z = eª + x + x* + 4 at the point (1, 0, 7).

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Q: 3. For f(x) =r² - 5x-6, make a table of slopes of secant lines and make a conjecture about the slope…

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Q: Find a such that the tangent lines to y = x3 − 2x2 + x + 1 at x = a and x = a + 1 are parallel.

A: Consider the function: yx=x3-2x2+x+1 Slope of a tangent at any point of a function is given by…

Q: Find an equation for the line tangent to the graph of 2x f(x) %3D x + 4 at the point (2,…

A: The standard form of the tangent helps to find the required equation. The standard form of the…

Q: Find all points on the graph of x2y − 2x + 63y = 2 where the tangent line is horizontal. (Enter…

A: Differentiate the equation x2y-2x+63y=2 wrt x:  ddxx2y-ddx2x+ddx63y=ddx22xy+x2dydx-2+63dydx=0

Q: Prove that the tangent lines to the curves 5y – 2x +y³ – x²y = 0 and 2y + 5x +x* – x³y2 = 0…

A: Given: - The statement is, The tangent lines to the curves 5y-2x+y3-x2y=0and 2y+5x+x4-x3y2=0…

Q: Show that if P lies on the intersection of the two curves x2 - y2 = c and xy = d (c, d constants),…

A: Given : The two curves x2 - y2 = c and xy = d intersect at point P where c and d are constants.…

Q: Prove that the inflection points of y = sin x are at the x-intercepts.

A: Inflection points are points where concavity changes that is where double derivative is zero

Q: Find an equation of the tangent plane to the graph of f(x, y) = xy3 + x2at (2, -2, f (2, -2)).

A: fx, y=xy3+x2 Partially differentiating with respect to x, keeping y as constant, we get fxx,…

Q: Find the value of c such that the line y = (1/6)x + (3/2) is tangent to the curve y = c(sqrt(x)).

A: Solution: Y1=16x+32Y2=cx

Q: Find a function f such that f'(x) = x“ and the line 2a - y = 3 is tangent to the graph of f. り

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Q: a point on the cor ve y=x² - 2x -3 at which is parallel to Find the tangent line the X-axis

A: Given query is to find the the point where tangent line paray to x axis.

Q: Determine the constant c such that the straight line joining the points (0,3) and (5.-2) is tangent…

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Q: Find all points​ (x,y) on the graph of y=x/(x−1) with tangent lines perpendicular to the line y=x−8.

A: The given function for the tangent is, Differentiate the above expression to get the slope of the…

Q: . Find all points (x, y) on the graph of f(x) = x with tangent lines passing through the point (3,…

A: Tangent line has an equation of line with slope equals to derivative of the function at that point.…

Q: Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y-2y³ In the…

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Q: , If the curves yı = -x² + ax +b and y2 x² + cx - 2 have the common tangent line at the point P(1,2)…

A: Given information: There are two equations  are y1=-x2+ax+b, y2=x2+cx-2 have a common tangent line…

Q: Find all points (x, y) on the graph of f(x) = x° - 4x + 20x + 11 with tangent lines parallel to the…

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Q: Find an equation of the tangent plane to the graph of f(x, y) = In(4x² – 2y2) at the point (1, 1).

A: To Determine: FInd the equation of tangent plane to the graph of…

Q: Find an equation of the tangent plane to the graph of f(x, y) = 4x² - 7xy² at the point (7, 8). z =

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Q: Find the slope of the tangent line to the graph r=2sin(0) at the point V3, 3 11.

A: We have to find

Q: %3D %3D .2 ,2.

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Q: Find a function f such that f'(x) = r and the line 4r - y = 3 is tangent to the graph of f.

A: Given: f'(x)=x3Tangent line to the given curve is:  4x-12y=3Therefore: y=8x-6

Q: Find an equation of the tangent plane to the graph of f (x, y) =2x2 - 4xy 2 at (-1, 2)

A: Given: f(x, y) = 2x2 -4xy2  To find: Equation of tangent plane to the graph of  f(x, y) = 2x2 -4xy2…

Q: Let f(x) = x² + 5x + 14. What is the value of x for which the tangent line to the graph of y = f(x)…

A: The slope of the tangent line to the curve is given by,…

Q: Find all points (x, y) on the graph of y = with tangent lines perpendicular to the line y= 4x - 3.…

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Q: Find the equation of the tangent plane to the graph of the curve f(x, y) = x² + y² at the point…

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Q: OShow that every point (b, c) in the plane lies on a tangent line to the graph of y = x³.

A: Consider the given information. y=x3 Find the derivative of the function. dydx=ddxx3y'=3x2

Q: Find the equation of the tangent line to the graph of the function f (z) = (z² + 10) (z – 2) at the…

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Q: The tangent plane to the graph of at the point where (x, y) = (2, 2) (write the appropriate function…

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Q: Let f(x) = 1x4 /4 + 2x3 – x2 + 3x + 7.                       a. Find f ’(x).  b. Find the equation…

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Q: Find an equation for the tangent plane to the graph of the function f (x, y) = y In(x² + 2y) + xy at…

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Q: Which of the following is/are points on the curve y = x4- 8x3 + 22x2 - 24x + 9 where the tangent…

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Q: Graph the function f(x) = are -2 , 0, and 1. 3x and draw the tangent lines to the graph at points…

A: Given: f(x)=-3x2 y=-3x2  x=-2,0,1x=-2 ⇒y=-3(-2)2=-12⇒(-2,-12)y=-3(0)=0⇒(0,0)y=-3(1)2=-3⇒(1,-3)

Q: Find the equation of the tangent plane to the graph of f(x, y) = 8x² – 2xy? at the point (5, 4). A)…

A: We first find the partial derivatives  So the direction vector of the normal is = (48,-80)

Q: The equation of the tangent line for the function f(x) = -3- 5x at z = 2 is %3D O y=-5(x- 2) – 13 O…

A: Equation of tangent line to a function f(x) at point ( x1,y1) is given by: y - y1 = m(x - x1) where…

Q: Find the tangent plane to the equation z = x2 + 5y² + 3y at the point (-5,-2,39)

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Q: b) Let f(x) = 4x - 2x - 5. %3D Find the intersection of the tangent line at c = 2 with the x axis.…

A: Given: The function fx=4x3-2x-5, To find: The intersection point of the tangent line at c=2 with…

Q: 7. Let f(x,y) = x²y+ry. Find an equation of the tangent plane to the graph of f at the point…

A: The detailed solution is given below Thank you

Q: If f(2) = -3, f'(2) = ÷ and g(x) = f¯(x), what is the equa %3D the tangent line to g(x) at x = -3?…

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Q: The tangent line to the graph of y = In(x² – 1) is perpendicular to the line z + y = -1lat the point…

A: Given: y=lnx2-1 and x+y=-1 Concept Used: Slope of perpendicular lines are negative reciprocal to…