true or false?  If the tangent line is horizontal then the function has a maximum or minimum value at the point.

Q: Use the graph to estimate the slope of the tangent line to y = x" at the given point. Verify your…

A: We have to tell the slope of the tangents through the graphs. So, for that, we will differentiate…

Q: a. Find the function f given that the slope of the tangent line to the graph of f at any point…

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Q: Differentiate (x-2)2+(y-3)2=9 at (7/2, ((6+3√3)/2)). Then use it to determine the equation of the…

A:

Q: Verify the tangent line approximation of the function at the given point. Then use a graphing…

A: To Find the derivative of the function :- To find the slope of the function at (0, 2)

Q: true or false?  A positive second derivative indicates that the curve is increasing from left to…

A: True or False A positive second derivative indicates that the curve is increasing from left to…

Q: orthogonal trajectories are curves in which their tangents at all points of intersection are at…

A: An Orthogonal Trajectory, of a family is defined as the group of curves that intersects each curve…

Q: Does the graph of -1, х 0 have a vertical tangent line at the origin? Give reasons for your answer.

A: Answer: No. The given graph of the function cannot have a vertical tangent line.

Q: Find an equation of the tangent line to the curve at the given point. y = 3x3 − x2 + 7,  (2, 27) y…

A: In

Q: Pregunta 8 Find the slope of the tangent line to the curve f(x) = x²(1 – æ)* at x = 2 Answer: The…

A: Product Rule of differentiation :   d(u.v)dx =u.dvdx+dudx.v

Q: Plot a function for which every secant line has a parallel tangent in between the points of secancy.

A:

Q: How can you use the slopes of tangents to determine whether a function is increasing, decreasing, at…

A:

Q: 24. At what point(s) on the curve (y - 2)² = x is the tangent line vertical? The tangent line is…

A: The given curve,   y-22=x

Q: Linearization based at a uses a tangent line to a curve at x=a to estimate the y-values of a…

A:

Q: 3e* at the point Estimate the slope of the tangent line of the function f(x) x=e (Use decimal…

A: Firstly, we find derivative of f(x) by using the result that derivative of e^x with respect to x  is…

Q: True or False 1) The peak of a smooth curve has a vertical tangent line. 2)The tangent line…

A: Given- Consider the given statement, 1) The peak of a smooth curve has a vertical tangent line.…

Q: 4. arctan (x + y) = y² , (1, 0)

A: tangent and normal line

Q: find the slope of the tangent to the curve y^2 + x^3+4=0 at (-2,2). Then find the slope of the line…

A:

Q: Find the slope of the tangent line to the curve 3 a -3 ry-3 y = -33 at the point (-2,-3). b) o d) e)…

A:

Q: What are the coordinates of the point on the curve f(x)=4/x^2  -x where the tangent is horizontal?

A: Given:  f(x)=4/x^2  -x

Q: Obtain the tangent line of the function y= 2x^2 + 3x + 2 at the point (1,7

A: Given: - The function is, y=2x2+3x+2 at the point (1,7) To find: - The equation of the tangent line…

Q: Find the slope of the tangent line using the Definition of a Tangent Line for: Y= x + 5X at the…

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Q: Find the equations of the tangent line and normal lines to the graph of the function f(x)=−2sin x…

A:

Q: Show that no tangent line to the graph of f (x) = tan x has zero slope. What is the least slope of a…

A:

Q: 1- Vx 6 Find the equation of the tangent and normal to the curve f(x) at the point 4, 5 1+ X

A: Given:     f(x) = 1 - √x / 1 + x  Points: ( 4 , -1/5 )

Q: True or false? The third derivative of position with respect to time is zero for an object falling…

A:

Q: A point of inflection on a curve is a point where y" is positive on one side and negative on the…

A: A point of inflexion is a point at which  y'' changes its sign. It is positive on one side and…

Q: Let y=4x4 + x. At what point is the tangent line to the graph perpendicular to the linet tangent to…

A: if line L1 having slope m1 and line L2 having slope m2 are perpendicular then m1m2=-1

Q: etermine the equation of the tangent line to the graph of f(x) = O y = 6 + 6x y=-6x - 6 Oy=6-6x x

A: Topic:- application of derivatives and integration

Q: Does the graph of -1, x0 have a vertical tangent line at the origin? Give reasons for your answer.

A: Given function is fx=-1, x<0   0, x=0   1, x>0.

Q: True or False? The Linear Approximation says that the vertical change in the graph is approximately…

A:

Q: find the x-coordinates of the point on the curve y=2x^3-3x^2-36x-1 where the tangent is horizontal.…

A: For finding tangent is horizontal take slope 0

Q: Write the application of Deravative" tangent and normal to a curve" also explain and with example.…

A:

Q: 5. Determine the slope of the tangent at point (1,5) on the graph of f(x) = (9 – x²)} + 1.

A:

Q: Is it possible to plot a function for which NONE of its secant lines has a parallel tangent line in…

A: Secant line is a line which cuts the function at minimum two points. Tangent line is a line that…

Q: true or false?  A negative derivative indicates that the curve is frowning.

A: TRUE Consider the graph for function x^3-x

Q: Find the tangent line to the curve 2y + " = ye"-2 at the point (2, ). %3D Please select file(s)…

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Q: + y3 equation of the tangent line to the curve x 4 at Find an (-3/3, 1).

A:

Q: Find the point (xo, yo) on the graph of y = x + 9x2 + 3x - 4, at which the slope of the tangent line…

A:

Q: Sketch level curve of f(x,y)=x2-y2

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Q: Find the equation of the tangent line to the curve y = x *sqrt(x2 + 5) at the point (2,6

A:

Q: Find an equation of the tangent line to the graph at the given point.

A: Given: 3 x2+y22 = 100 x2 - y2  and the point (4, 2) To find: An equation of the tangent line to the…

Q: Determine the slope of the secant between x = 3 and x =8 for the function f(x) = 2x3-7x. .B Draw a…

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Q: 13. BONUS: Find the coordinates of all points on the graph of y=1-x at which the tangent line passes…

A:

Q: The straight line y=x +B is tangent to the graph of f(x) = 2^{x at the point where x = A. Find A and…

A: The staright line y=13x+B is tangent to the graph of f(x)=2x at the point where x = A, we have to…

Q: Is it possible to draw a tangent line with slope 4 to a differentiable function f which passes…

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Q: What’s the equation of the tangent line to the curve y = 5ln(x^3 - 7) at the point (2,0)

A:

Q: Find equations of all tangents to the curve f(x) = 4/x that have slope -1. Options attatched

A: f(x) = 4/x                    Slope of tangent = -1

Q: roblem 5. Find the equation for the line tangent to the curve y√ = 3x√√y - 10 at x =

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.