If y=mx+b is the equation of the tangent line the curve y=x2-3x+5 , which is parallel to the secant line of the curve at x=-2 and x=3, then the slope m is [m] and the y-intercept b is [b]. m= b=

Q: Find the equation of the tangent line to the curve y = x² – 5 if the tangent lir is parallel to the…

A: we know that if two lines are parallel then their slopes are equalGiven that the tangent line is…

Q: 3. Find the equation of the tangent line to the curve y = x2 – 3x + 4 that is perpendicular to the…

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

Q: Find an equation of the line tangent to the curve defined by z2 + 6ry +y = 32 at the point (2, 2).

A:

Q: 7. Find the slope of the tangent line to the graph at (1,1): x²y² – 9x² – 4y² = 0 %3D r-9r-4y = 0…

A: find the slope of the tangent line to the graph at 1,1; x2y2-9x2-4y2=0 differentiate the equation…

Q: 4. Find the equation for the line tangent to a. y=x²- 3 x + 5 at the point (2, 3)

A: We will find tangent equation.

Q: [3] If the curve is defined by y = x* – 8x3 + 22x2-24x+9, then what are the value/s of x for which…

A:

Q: If y=mx+b is the equation of the tangent line the curve y = x- 3x +5, which is parallel to the…

A: We will solve the problem

Q: At what point on the curve x 3t2 + 1, y = t3 - 5 does the tangent line have slope ? (х, у) -

A: We have given curve as x=3t2+1         ⋯⋯1y=t3-5           ⋯⋯2 From the equation (1) and (2), on…

Q: 3. Find the equation of the tangent line to the curve y = x2 - 3x + 4 that perpendicular to the line…

A: we have to find the equation of the tangent line to the curve y=x2-3x+4 that is perpendicular to the…

Q: 5. Find the equation of the tangent lines to the curve y = x² + 3x -4 and parallel to the line 6x…

A:

Q: FInd the equations of the tangent lines to the curve y=(x-5)/(x+5) that are parallel to the line…

A: Given:The equation of the curve is y =(x-5)/(x+5).The equation of the line is x-10y =2.

Q: B. Find the slope and the equation of the tangent line to the curve 1. y = 4 - 3x at (- 1, 1) 2. y…

A: We need to find the slope and the equation of the tangent line tothe following curve:3. y=3x2+2 at…

Q: Find the equation of the tangent line to the graph xy^2 − 2y = x^2 at the point (2, −1).

A:

Q: Find y' and the slope of the tangent line to the graph of (3x- 2y)° = 2y2 - 9 at the point (1,2).

A:

Q: Find an equation for the tangent line to the graph of y – 3xy + x2 +1 = 0 at the point (2, 1).

A:

Q: At what point on the curve x = 3t2 + 2, y = t3 – 2 does the tangent line have slope ? (х, у)

A: Slope of the line = dy/dx To get dy/dx, first get dx/dt then get dy/dt. Now divide dy/dt by dx/dt.5

Q: Find an equation of the tangent line to the graph of the equation x2+9xy +y2 =25 at point (0, 5)

A:

Q: At the two points where the curve x² – xy + y² = 36 crosses the x-axis, the tangents to the curve…

A: Given equation of the curve is: x^2 - xy + y^2 = 36 ..................... (1) Differentiating above…

Q: Find the equation of the tangent line to the graph of y = 2x - (4 / √x) at the point (4, 6).

A: Given,            y = 2x - 4x and Point is 4, 6

Q: Find an equation of the tangent line to the curve x2+y+y2=13 at the point (-1,3)

A:

Q: Find an equation for the line tangent to given curve y = -10z2-3 4r+1 3 at x = 0-

A:

Q: 3. Find the equation of the tangent line to the graph of x y + 7xy = 30 at the point (-5, 2). %3|

A:

Q: Find an equation of the tangent line at the point indicated. x3y + y3x = 10; (1,2)

A: Given query is to find the equation of the tangent line at (1,2).

Q: Find the equation of the tangent line to the curve x2 + 4y2 = 8 and parallel to the line x+2y=8.

A: Given curve is x2+4y2=8. To find equation of tangent line to the given curve which is parallel to…

Q: Find the equation of the tangent line to the graph of 3x- xy + y - 9 = 0 at the point (2, -3).

A: The graph of 3x3-x2y+y3-9=0 at the point 2,-3

Q: What is the slope of the tangent line that touches the graph of In(y) +e-'=3y – 4x at the point.12

A:

Q: Find the equation of the tangent line to the curve at the given point. y = /2x +1, (4, 3)

A: To find the slope, we find dy/dx at (4, 3) At (4, 3):

Q: Find the equation of the tangent line to the graph ofx^2 * y^2 + 3xy =18 at the point (-2, 3)

A: The given curve is: x2+y2+3xy=18 Differentiating both sides of the equation with respect to 'x', we…

Q: 1 Find the two points on the curve y=- at which the tangents have as slope of -.

A: Given,            The curve y=1x at which the tangents have as slope of -12.To find : The two points…

Q: Find the equation of the tangent line at the point (1,−3) to the curve defined implicitly below. x3…

A: The line is tangent to the given hyperbola at (1,-3).Tangent line is a straight line.Therefore, the…

Q: Find the two points where the curve x2 + xy + y2 = 7 crosses the x-axis, and show that the tangents…

A: To determine the x-intercept of the curve and slope of the tangent at the intercept.

Q: 4. Find the equation for the line tangent to a. y= x²- 3 x + 5 at the point (2, 3)

A:

Q: 25. Find the equation of the line tangent to the curve x2 + y2 = 1 through the point (,).

A:

Q: What is the slope of the tangent line that touches the graph of In(y)+e2x-=3y – 4x at the point (A 1…

A: The solution are next step

Q: 2. At which points on the curve y = 1+ 60x – 2x does the tangent line have the largest slope?

A: Solution ) y = 1+60x3- 2x5 First derivative with respect to  x y' =0+ 60 ×3 × x2 - 2×5 x4 y' = 180x2…

Q: Find an equation of the tangent line to the curve at the given point. y = 3x - 14x + 1, (5, 6)

A:

Q: 1 - Find the equation of the tangent line to the curve y = 3 5 x2 +6x 2 11 at its point of…

A:

Q: Find the equation of the tangent line to the curve y= 3x^2 - 2 passing through the point P(-1,1) .

A:

Q: Find the points on the graph of x5/2 + y5/2= 1 where the slope of the tangent line is -1.

A: Topic:- application of derivatives

Q: The slope of the line tangent to the curve y = x*- 8x3 + 22x² – 24x + 9 at x = 1 is _.

A:

Q: What is the slope of the tangent line that touches the graph of In(y) + eA-=3y-4x at the point 3. 5

A:

Q: 4. Find the equation of the tangent lines to the curve y = √x and perpendicular to the line 14x +…

A: We have to find the tangent

Q: Find an equation of the line tangent to the curve defined by x^3+2xy+y^3=4 at the point (1,1).

A: To find the equation of the tangent line at the point (1, 1) to the curve given below.

Q: Find an equation of the line tangent to the curve defined by x^3+6xy+y^5=21 at the point (2,1)

A:

Q: At what point (x,y) is the tangent line to the curve y=2x2-5x+8 parallel to the line y=3x-7

A: It is given that

Q: 2. Determine the equation of the line tangent to the graph of y = x³ + 2x at the point (1,3).

A:

Q: 1) Find the slope of the line tangent to the graph of y=x²+1at(2, 5).

A:

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

A: here given y= (3x+4)3 slope  of the tangent line is y'    Here y' = 9(3x+4)²   Value of y at x=-2 is…

Q: find an equation for the line tangent to given curve at the given value of x. y=x-x2 ;x=-2

A:

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.