Let a be a real number and a and B the roots of x'- 2a'x+1= 0. Show that attains a' a minimum value.Find the minimum value and the roots for which it has attained.

Q: Where does a local minimum occur?

A: given,      Local minimum .

Q: Two nonnegative numbers whose product is 25a² (where a 0) and whose sum is a minimum, are

A:

Q: The slope of the tangent line to the parabola y = 2x + 5x + 7 at the point (- 4, 19) is: The…

A:

Q: Prove that Pr (|X − a| < τ ) takes its maximum value when a = µ where X ~ N (µ, σ2)

A:

Q: Find the positive number x such that the sum of x and its reciprocal is as small as possible. Does…

A: Given the positive number is x

Q: Find the equation for the perpendicular trajectories of the curve family. 1. x -

A:

Q: Find the point (xo, yo) on the graph of y = x' + 9x² + 6x – 3, at which the slope of the tangent…

A:

Q: Find the minimum and maximum values of the function y = 1613 + 2412 on [1,2] by comparing values at…

A: The given function y=16t3+24t2 on 1,2

Q: Find all the points on the graph of (x² + y²)² = x² – y² that have horizontal tangent line.

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Find the absulote maximum of x40-x20 on the interval [0,1],also find its absolute maximum value

A:

Q: Find two positive numbers with product 289 and whose sum is a minimum.   Enter your answers in…

A:

Q: The slope of the tangent line to the parabola y 2x + 3x +6 at the point (1, 11) is: The equation of…

A:

Q: Find the minimum and maximum values of the function y = 2613 + 39t² on [1,2] by comparing values at…

A:

Q: Sketch the graph of a function on [-1, 2] that has anabsolute maximum but no absolute minimum.

A: According to the given information, it is required to sketch the graph of the function on [-1,2]…

Q: Find the absolute minimum value for on the interval [-1,1]

A: In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol…

Q: Find the orthogonal trajectories for the family of curves 3x2 − y2 = C. Use a graphing utility to…

A: Given:  The family of curves: 3x2 − y2 = C

Q: Find the maximum area of a triangle formed by the axes and a tangent line to the graph of y = (x +…

A: Find the maximum area of a triangle formed by the axes and a tangent line to the graph of y = (x +…

Q: Find the absolute maximum and absolute minimum values off on the given interval. Ax) = (x²-1)°,…

A:

Q: I dont know where to start this problem. It would be great to have some help

A: Given:

Q: The length and width of a rectangle are measured as 35 cm and 28 cm, respectively, with an error in…

A: To determine the maximum error in the area.

Q: Find a parabola with equation y = ax2 + bx + c that has slope 5 at x = 1, slope −11 at x = −1, and…

A:

Q: If the function tends to infinity at the endpoints of the interval, then the function must take on a…

A: A continuous function defined on open interval with range equal to a closed interval. Consider a…

Q: The length and width of a rectangle are measured as 25 cm and 36 cm, respectively, with an error in…

A: Given length of a rectangle, l =25 cm           Width of a rectangle, w=36 cm We know that,  Area of…

Q: Does ƒ(x) = (7 + x)(11 - 3x)^(1/3) have an absolute minimum value? An absolute maximum? If so, find…

A: Check the function has absolute minimum value.

Q: The slope of the tangent line to the parabola y 3x2 + 2x + 6 at the point (5, 91) is: The equation…

A:

Q: Find the point (xo, yo) on the graph of y = x + 3x² + 4x – 5, at which the slope of the tangent line…

A:

Q: Find the point (s) on x = 3 - y2 that are closest to point A = (1,0).

A: Given: x = 3 - y2 and point A = (1, 0)

Q: Find the point (x0, yo) on the graph of y = x + 9x² + 8x – 5, at which the slope of the tangent line…

A:

Q: 8. Find the point on the curve y = √2x 3 from the point (1, 4)-

A:

Q: maximum of the quantity xy2 where x and y are

A:

Q: Find the critical points of y= -2x^2 +4x +3 and apply the Second Derivative Test to find the maximum…

A: Critical point and extreme points

Q: Find the point (xo, yo) on the graph of y = x + 3x2 + 5x – 3, at which the slope of the tangent line…

A:

Q: Find all points on the curve 3x + 6y² = 36 where the tangent line also passes through the point (10,…

A:

Q: at 2 Find absOIute maximum & minimum value fu)=x²-1 on [lile)

A:

Q: Explain theorem of Wronskians of Solutions?

A: To Find : Define the Theorem of Wronskians of solution

Q: Find the fourth iteration value in finding an extremum (maximum/minimum) value of              f(x)…

A: The Newton Raphson method is used to solve an equation numerically. When the extremum of a function…

Q: 1. Find two non-negative numbers whose sum is 12 such that their product is an absolute maximum.

A: Let x and y are two non-negative numbers. We have to find maximum of the function Fx,y=xy It is…

Q: Function f(x) is defined as f(x) = x3 + 2x² - 20x + 10 in interval [-2, 1], what willI be it's…

A: Introduction :

Q: Find the x-coordinates of all points on the curve y = 12x" - 96x° - 168x + 26x + 91 where the…

A:

Q: (x) = 5sin2x

A:

Q: local

A:

Q: 2. Find an equation of a curve satisfying the ff. condition and passing through the point (0, -1).

A: dxy-dy1+x3=0A first order separable ODE has the form of Ny·y'=MxLet y be the dependent variable.…

Q: Find the fourth iteration value in finding an extremum (maximum/minimum) value of              f(x)…

A:

Q: 5. Find the point on the parabola y=2x-3x+6 where the tangent line is parallel to the line 7x+y=1.

A:

Q: Let y=X^x, X&gt;0. Find the x where the function has a minimum value What is this minimum value?

A:

Q: is the total cost of production for a 7-hour day, where x machines are used to produce jackets and y…

A: The Extreme value theorem states that if a function is continuous on a closed interval a, b, then…

Q: Find the point (xo, yo) on the graph of y = x' + 9x² + 7x – 5, at which the slope of the tangent…

A:

Q: The length and width of a rectangle are measured as 38 cm and 34 cm, respectively, with an error in…

A:

Q: Find the equation of the tangent line to the function f(x) = 8/x - 2 at the point (64, 62). Provide…

A: To determine the equation of the tangent in the form y =mx+b

Q: What conditions must be met to ensure that a function has anabsolute maximum value and an absolute…

A: Given, To write conditions that must be met to ensure that a function has anabsolute maximum value…