8: What are the values of k E R for which the function f(X) = -2kx² + x₁x² + 4x will have a strict local minimizer at x = [ko] ? A: k <2 B: k = 0 C: k<0 D: k> 0 Ο Α A О в О с O D O O

Q: 4. What function is y = x3 + 2r + 1? * O A. Linear Function O B. Polynomial Function C. Quadratic…

A:

Q: 5. The function f(x) = (x+ 5)(x- 3) is dilated by x to produce the function g(x) = x f(x). How many…

A:

Q: Q1. How many pairs of ordered numbers exist such that their sum, product, and quotient are the same?

A: Keeping a note, according to our guidelines we can only answer one question, kindly repost other…

Q: 3. Let f(x) = x - r - 3x. Determine the interval(s) on which f(x) is increasing and the interval(s)…

A: To find the points of minima and maxima first we need to find the critical points of function by…

Q: Find the absolute maximum and absolute minimum of the function f(r) =r² - 8z+7 over [1, 8].

A:

Q: Find the point on the graph of y = 1x that is closest to the point (2, 0). [Hint: 2(x - 2)2 + y2 has…

A: Given: y=x Let the point closest to (2,0) be P(x,y). Distance between point P(x,y) and (2,0) is:…

Q: Find the maximum value of f(x)=−5x2+5x+6 on the interval [−20,20]

A:

Q: 1. Find the fixed point(s) of the function g(x) = 32³-62²-1+4 on the interval [0,4]. (Answer: √2/3,…

A:

Q: Find Əf ax and Əf Əy 2 f(x,y) = √2x² + y²

A:

Q: Suppose that x and y are two positive real numbers so that x + y = 10. Maximize the product xy

A: To find the solution of the given problem use the second derivative test. Second derivative test:…

Q: Find maxima, minima, and chairs of the function f (x,y) = (x² + y²)e(x+y) x² + y² < 4. in the region

A: The given functionisfx,y=x2+y2ex+y.To find the maxima, minima and chairs of the functionin the…

Q: 2. For a given function f(x) -(x – 2)2 + 6 a) Axis of symmetry : x= b) The vertex (h,k) is: c)…

A:

Q: 1. Find the domain of f(x) = v2 + 5.x – 3x².

A: The domain of a function is the set of input or argument values for which the function is real and…

Q: Q3) Find the minimum of the Brown's badly scaled function using Powell's method. f(x) = (x₁ - 106)²…

A: We will use the basic knowledge of partial derivatives and differential calculus to answer this…

Q: 3. The diagram on the right shows an open box with a square base of side x cm and a height of h cm.…

A: a)Area of the box (A)=x.x+2xh+2xhA=x2+4xh75=x2+4xh  [Since A=75 cm2]75-x2=4xhh=14x75-x2Volume of the…

Q: -. Which equation shows the minimum or maximum value of f(x) without changing the form of the…

A: Please refer the attached image for complete solution.

Q: What function should be used to minimize the distance between y = x + 5 and the point (3, 1)? O D(æ)…

A: Explanation of the solution is given below...

Q: 7. Which vertex will result in the maximum value of the function T = x - 3y? O (3.5, 4) (0, 4)

A: Answer and explanation is given below..

Q: 16. Let f(x) = x² + 10x + 28 m, find m if the function only has 1 (ONE) x-intercept. -

A:

Q: 4. Are the following functions cubic splines? a. f(x) - x- 2x + 3, 0 sxs 1, - 2x - 3x2 + x + 2, 1 s…

A: Given :(a) f(x)=x3-2x+3, 0≤x≤1             =2x3-3x2+x+2, 1≤x≤2(b) f(x)=5x3-3x2+1 0≤x≤1…

Q: Consider the function 2² + 2x +1 y = r2 +1 a) Show that the domain of this function is a €R. b) Find…

A:

Q: 10. Find all relative maxima of the given function. y =x* -8x +16x² +10 A) (0,10) B) (2,26) C)…

A:

Q: Given the function f (x) = ax + x2 for all x + 0 and f (1) = 3. %3D a) Find the values of a and b.…

A: Given function is, f(x)=ax+bx2 We use first derivative test to find stationary points.…