On the interval 0 < x < 3, the function f (x) = x² – 8x + 16, which one it is  a) is concave down  b) is always decreasing  c) is always increasing  d) has a local minimum

Q: 5. Determine the minimum value of f(x) 3x on the interval [-1,1] %3D

A: Let's find.

Q: 2- find the absolute max.and min. of the on the closed triangle function P : x* + y Plate bounded by…

A:

Q: find the maxim um anel minimum Limits of the functibu :- Fixy) = x"; + y- 2x-4xy-2y?

A:

Q: The function f(x) = xvx – x² defined on the closed domain [0, 0.9] has an absolute minimum value of…

A:

Q: Suppose that f(x, y) = 5x + 2y at which - 4 < x < 4, – 4 < y < 4. %3D Absolute minimum of f(x, y) is…

A:

Q: Show that the limit of the function f(x,y)= (0,0). (x+y)² x² + y² is indeterminate at

A: Limit of the function

Q: The f(x) 6x2 -5x-4 2x2 +x is discontinuous %3D at x = -1/2. By redefine = w , then f will be…

A:

Q: 2. On the interval [0,2], determine the absolute maximum, M, and absolute minimum, m. fx) 4x

A: Given fx=4x1+x2 on 0,2

Q: Consider the problem of finding the local minimum points of the function f(ï) = -4 +" over the…

A: Given

Q: If f, (a,b) = f, (a,b) = 0, does it follow that f has a local maximum or local minimum at (a,b)?…

A: Given, fx(a,b)=fy(a,b)=0

Q: Prove that if f(x)>0 and f′(x) exists for all x in the interval [a,b] then the square root  of f(x)…

A: Given: Prove that if f(x)&gt;0 and f′(x) exists for all x in the interval [a,b] then the square root…

Q: Let A be a positive real number. If the absolute minimum value of f(x) Ar5 35x on [0, oo) occurs at…

A: If the absolute minimum value of f(x)=Ax5-35x3 on [0,∞) occurs at x=cAk. Where A be a positive real…

Q: Suppose that f(x, y) = 5x + 2y at which -4 < * < 4, – 4< y < 4. Absolute minimum of f(x, y) is -28…

A:

Q: Given ƒ(x) = ax2 + 2bx + c with a &gt;0. By considering the minimum, prove that ƒ(x)&gt;= 0 for all…

A: Consider the given function f(x) = ax2+2bx+c with a &gt; 0It is required to prove that:

Q: Let f(x) = x³ - 3x². Find the absolute minimum value of f(x) on the interval [1, 4].

A: The given function,  f(x)=x3-3x2 on the interval 1,4

Q: Let f(x) = x²+x+ 2 = Z₂ (x) prove that f(x) irreduciable Poly

A: The given function is  f(x)=x2+x+2.

Q: ind the maximum of all the possible value

A:

Q: Let A be a positive real number. If the absolute minimum value of f(x) = Ax³ – 40x³ on 0, 00) occurs…

A: fx=Ax5-40x3 Differentiating with respect to x, we get f'x=A·5x4-40·3x2=5Ax4-120x2 Now to find…

Q: Let A be a positive real number. If the absolute minimum value of f(x) = Ax³ – 90x³ on [0, 00)…

A: we  are given f(x)=Ax5-90x3 and absolute minimum at x=cAk we have to find c?

Q: Give an example that: the f'(c) 0 but c is not a local maximum or local minimum.

A:

Q: Соpy of The global minimum of f(x) = x³ – 4x over the interval -2< x<3 occurs at what value of x? O…

A:

Q: Let f(x) be maximum and g(x) be minimum of {x|×|, x² | × [} then

A: 9

Q: Let f(x) be maximum and g(x) be minimum of {x|×|, x² |x} then

A:

Q: By choosing x, find a maximum of xre-x, if r>2, otherwise the function goes to infinity at x=0.

A:

Q: Suppose that f(a, b) is an absolute maximum of the function f (x, y). Must f (a, b) also be a local…

A: First of all, undrstand the difference between absolute maxima and local maxima.Let, z = f(x,y)…

Q: Consider the cubic functionf (x) = ax3 + bx2 + cx + d, where a  0. Show that f canhave zero, one,…

A: We have fx=ax3+bx2+cx+d This implies  f'x=3ax2+2bx+c Set f'x=0 i.e 3ax2+2bx+c=0 and solve it using…

Q: Which is not true? If a function is continuous on a closed interval [a,b], then it has a maximum and…

A:

Q: Find the absolute maximum of p(x)=x2 −x+2 over [0,3].

A: We have to find absolute maximum of f(x) in given interval .F(x) is given as:

Q: Prove that if A has n as a minimum then B = {x ∈ R | ∃a ∈ A, x = −3a} has −3n as a maximum

A:

Q: 5. Verify first that the Intermediate Value Theorem applies to the indicated interval and find the…

A:

Q: 2. Suppose that f (a, b) is an absolute maximum of the function f(x, y). Must f (a, b) also be a…

A:

Q: Suppose that ƒ(x) = x2 and g(x) = | x | . Then thecompositions( ƒ ∘ g)(x) = | x | 2 = x2 and (g ∘…

A: Given: The composite of the two functions are given as,

Q: Determine the maximum value of f (x) = 5x – e5x [T:3] on the interval [-1,1] %3D

A:

Q: The absolute minimum of f(x) =x² – 4x On [0,3] is y= %3D 540 .BO -4 .CO -3

A: We use first derivative test to find absolute minimum.

Q: Let f(x) = -2x' +3x² +1 on Find the critical numbers for y = f(x), and show how you use the Closed…

A:

Q: Use calculus to find the x-locations of the local maximum and local minimum values of S(x) = (½)x°…

A:

Q: Let A be a positive real number. If the absolute minimum value of  f(x)=Ax^5−25x^3 on [0,∞) occurs…

A: A be a positive real number.  absolute minimum value of f(x) where  f(x)=Ax^5−25x^3 on [0,∞) occurs…

Q: Find m so that f(x) is continuous at x = 2. x +4 if x 2 -

A:

Q: what is the absolute maximum/minimum of: f(x)=xln(x/4) on [0.2,4]

A: Given, function is

Q: Suppose that f(x, y) = 5x + 2y at which – 4 < x < 4, – 4 < y < 4. %3! Absolute minimum of f(x, y) is…

A:

Q: -- ) Determine the values of constanas a, b, c, and d so that f(x) = ax³ + bx² + cx+d has a local…

A: As given (0, 0) is a point of local maximum and (1,−1) is a point of local minimum of f(x). The…

Q: 2. Use the Intermediate Value Theorem to prove that the equation e* = 4 - x³is solvable on the…

A:

Q: If x = c is in the domain of f such that f'(c) = 0 and f"(c) > 0, then f has a local maximum at x=…

A: The given problem is solved below in detail.

Q: 2. Consider a function f : R → R where S(x) = x³ – 3x for all æ e R. Identify all critical points…

A: Given the function fx=x3-3x  ,x∈R. To find the critical points and the local maximum and local…

Q: If f has an absolute maximum value over a closed interval [a, b], a, b e R at x = xo, where xo E (a,…

A: Topic:- function

Q: Let f(x) = 2 cosh(4x) – e4x %3D Find the absolute maximum of f(x) on the interval [0, In 3].

A: The given function is                                         f(x)=2 cosh(4x)-e-4x We know that…

Q: Suppose that the function f: R → Ris continuous and that its image f (R) is bounded. Prove that…

A:

Q: What are the absolute maximums and minimums of z(x) over its domain?

A: Given To find what are the absolute maximums and minimums of z(x) over its domain.

Q: ) Find all critical points of f(Xiy> and dlassify each as a celative maaimum, celatine minimum, or a…

A:

Q: 2: Find the minimum value of f on the closed interval [-3,8]. Justify yokr answer..

A: To find the minimum value of f on the closed interval -3,8