33. (a) The curve with equation y² = 5x* – x² is called a kampyle of Eudoxus. Find an equation of the tangent line to this curve at the point (1, 2).

Q: 8. Estimate the slope of the tangent line to the curve y = -2x at x=-4, and then use it to find the…

A: Given curve is y=-2x3 To find the slope of tangent at x=-4. Solution: Differentiating the given…

Q: 4. Find the equation of the tangent line to the curve y=x-2x+3 at the point (2,3).

A:

Q: 5. Find the equation of the tangent line that passes through point (1,2) to the graph 8y3 + x²y – x…

A: Proceed as shown below...

Q: 4 The slope of the tangent line to the curve y = X at the point 5, is: 5

A:

Q: 4. Find the slope of the tangent to y = sin² (2x) at x = 12

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Q: 4. Find the equation of the tangent line to the curve y = 5x– 6/x at the point (1, –1).

A:

Q: At what point on the curve  y = 6 + 2ex − 3x  is the tangent line parallel to the line  3x − y =…

A:

Q: Find the slope of the tangent line at the point P = (1, 1) on the graph of              ex-y = 2x2 -…

A: Given,          ex-y = 2x2- y2    at   P=(1, 1)

Q: 5. Write the equation of the tangent line to the curve of y = e³x + cos(-x) at the point (0,2).

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Q: 9. Find all the x-values on the curve where the tangent line is horizontal Y = 2x°(x- 3)°

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Q: -1 Where on the curve y = (256+ x²)¯* does the tangent line have the greatest slope? NOTE: Enter the…

A:

Q: Find the equation of the tangent line at the given point on curve.

A:

Q: Find the slope of the tangent line to the curve defined by 4x + xy – y* 1760 at the point (8, –4). e…

A: To find the slope of the tangent line to the given curve at the given point

Q: 9. Find equation of the tangent line to the graph of x* +y+xy' = 3 %3D at the point (1,-2)

A:

Q: y = 16 X + x² at x at x = 4.

A: Given Equation :- y=16x+x2  Find the equation for the tangent line to the curve at x=4

Q: 3. Find the equation of the tangent line to the curve x'y+y°x= 30 at point (1,3).

A: Solve the given problem.

Q: Find the equation of the tangent line to the curve x4+y4=2 at the point (1,1)

A:

Q: 9. Find the equation of the tangent line at point (2,2) on the curve fx) = x²- 7x + 12.

A: To find the equation of the tangent line

Q: Find the equation of the tangent line at the given point on curve. x2 + y2 = 25; (-3, 4)

A: Given: x2 + y2 = 25; (-3, 4)

Q: Find the slope of the tangent line to the curve defined by 4x + xy – y = 1760 at the point (8, –4).…

A:

Q: The slope of the tangent line to the curve x^3 + y^3 = 6xy at the point (3,3) is

A:

Q: 4 at the point ( 6, The slope of the tangent line to the curve y is: 3 |

A: The  Slope of the tangent line is = -(1/9)

Q: 3. Find an equation of the tangent line to the curve at x=4 y=(sqrt(x)) / (x+6)

A: Given equation of the curve y = xx+6  ...............(1) Let the equation of the tangent at (x1, y1)…

Q: What is the value of the slope of the tangent line to the curve *y+y²=5 passing through the point…

A:

Q: Find the slope of the tangent line to the curve 2² – -1 4.xy + 4y: at the point (1, - 1),

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Q: Find the equation of tangent line to the curve at the given point x2 + 2xy - y2 + x = 2 (1, 2)

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Q: 3 at the point ( 6, (0.) The slope of the tangent line to the curve y = is:

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Q: 4 at the point ( 3, The slope of the tangent line to the curve y is:

A:

Q: 2 Write the equation of the tangent line to the graph of y =x at the point x = - 0.7.

A: Given equation is To find the equation of tangent line y=mx+b, we need to find out the slope m…

Q: tangent line

A:

Q: 9. Find the equation of the curve whose y" e*. = - cos x + 6x + 4 with horizontal tangent at the…

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Q: The equation of the tangent line to the curve: y + 5 = 2x at x = 5.

A:

Q: 4. Find an equation of the tangent line to the curve x – 1 | at the point (3, 2). ||

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: 2) Find the tangent line to y2 = x at the point (4, –2).

A: Given: y2=x…

Q: 4. The slope of the tangent line to the curve y 4. is: 9 - at the point 9, The equation of this…

A: To find the slope of the tangent line to the curve, y=4x, at the point 9, 49.The  equation of this…

Q: 2) Find the equation of the tangent line in slope intercept form to the curve x² + 4xy + y2 = 13 at…

A:

Q: curve at the following point:  y = 2/ 1 + e-x, (0,1)

A:

Q: What is the value of the slope of the tangent line to the curve x²+ 4.xy +y² =13 passing through the…

A: topic - slope of a tangent at a point on a curve

Q: -1 Where on the curve Y (1+ x2)¯ does the tangent line have the greatest slope? NOTE: Enter the…

A: Given:- y = (1+x2)-1 To find:- Point where tangent line on given have greatest slope

Q: 5- Find the slope of the curve and the tangent line of y = 2x- 3 at (0, 2).

A:

Q: Show that the curve y = 6 x 3 + 5x -3            has no tangent line with slope 4.

A: y=6x3+5x-3 has no tangent line with slope 4

Q: 3 - at the point (3, 1) is: The slope of the tangent line to the curve y The equation of this…

A:

Q: Determine the slope of the tangent line to the curve (x² + y² – 2x)² = 2(x² + y²) at (2, 2).

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Q: Find the slope of the tangent line to the curve given by y^4 = y^2 - x^2 at the point (0,1)

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Q: Find the slope of the tangent line to the curve defined by 9a – 8zy – y* = -18 at the point (-1,…

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Q: Find the equation of the tangent line to the curve y = 2 In(x³ – 26) at the point (3, 0). y =

A:

Q: Find an equation for the tangent line to the curve y = 2/x at the point (2, 1) on this curve.

A: Given, Equation of curve : y=2x      (i) Common point = (2,1)

Q: 4. Find the equation of the tangent line to the function y = In (x² – 2) when x=3.

A: Question is solved.

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.