(a) Let f(x) = px² + 2qx +r with p > 0. By considering the minimum, prove that f(x) > 0 for all real x if and only if q² – pr < 0. %3D

Q: a) Find the local maximum and minimum value(s) (if it exists) of the function f(x, y) = 4x + 6y - x²…

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Q: Find a cubic function f(x)  = ax3 + bx2 +cx +d thathas a local maximum value of 3 at x =-2 and a…

A: At x=-2 , y=3  So,  at x=1, y=0

Q: Consider an arbitrary quadratic function f(x) = a.x² + bx +c where a, b, and c are constants with a…

A: We need to find second derivative test to check local maximum and minimum

Q: Find the local maximum and local minimum in (x,y) notation for the following: y=(2x2-7x)/(2x+5)

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

A: Given

Q: Find the values of constants a, b, and c such that the graph ofy = (x2 + a) /(bx + c) has a local…

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Q: Find the critical points of f(x) = x* – 4x + 2, and identify each as a local minimum, a local…

A: For the function f(x)=x4-4x3+2, to identify the critical points, we will use second order derivative…

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: 9- Find the coordinates of the absolute maximum an d minimum points for f(x)=2x²-x* given x €[0,4] :

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Q: 1 Use the maximum-minimum principle 1 to Find absolute maximum and minimum Of the function: F(x)= x3…

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Q: Find the critical points for the function f (x, y) = x³ + ³ – 6x2 – 3y – 6 and classify each as a…

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Q: Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 2 at x = −2 and a…

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Q: if f'(x) = x(x-1)(x+3)4 , then f(x) has a local minimum at

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Q: Find the location of the minimum absolute extremum for A. No minimum the function. В. х%3D — 1 Af(x)…

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Q: 9. Determine all of the local minimum points, local maximum points, and saddle points for the…

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Q: find all critical points of the function f (x, y) = x³ + y³ – 3xy - and determine if they are local…

A: Given: fx,y=x3+y3-3xy So, fx=3x2-3y, fy=3y2-3x To find critical points, put fx=0 and fy=0 Now,…

Q: 3. Find all the critical points of the function f(x, y) = e(x² + y²) and determine whether each of…

A: Given function is f(x, y) = ey(x2 + y2)

Q: Find the quadratic function f (x) = ax2 + bx + c that goes through (0, 1) and has a local minimum at…

A: Given: The quadratic function fx=ax2+bx+cpasses through the point 0,1 and has local minimum at 1,-1,…

Q: 1. Find the absolute minimum and absolute maximum of the function f(x) = 2x-3x? on the closed…

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Q: f(x) = 3 x4-4 x3 -12 x2+1, has local minimum at x = OA. OB 2- OC. OD.

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

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Q: f(x) = -8x + 1 has a: %3D O maximum neither a minimum or maximum O minimum

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Q: Find the absolute extremum within the specified domain. 21) Minimum of f(x)=(x2+4)2/3; [-2,2]

A: According to our policies we are allowed to solve one question at a time. Kindly repost other…

Q: Let g(x) = x4 – 2x2 + 1. (a) Find all critical points of g. (b) Find the absolute maximum and…

A: Use derivative

Q: 8. Find the local minimum and the local maximum and saddle points of f (x, y)= x² + y' - 3x² - 3 y²…

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Q: Find the global maximum and global minimum of f(x)=2x in the interval [−1,3].

A: Given function is Differentiating with respect to x, we get Now, f'(x) =0 for no value of x and…

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: Find the absolute minimum value on (0,infinity) for f(x)=4e^x/x^2

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Q: Let f(x, y) = x² - 4x + y + 9. Find the absolute maximum and absolute minimum of f(x, y) restricted…

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Q: Find all the critical points of the function and determine at each one whether there is a local…

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Q: 3. Find the Absolute Minimum and Absolute Maximum of f(x,y)=xy subject to 2x² +8y² =144 Fully…

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Q: Suppose f'(x) =x++x³- 6x². Determine the value of x where f has a relative minimum value. x= - 3 O…

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

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Q: find the formula for a function of the form f(t)=at+b/t with a local minimum at (3,3) and a local…

A: For critical values of f(t), f'(t)=0Critical values of f(t) are t=-3 and t=3So we find f'(t) from…

Q: Find the absolute maximum and absolute minimum of  g(t) = t(square root of 4-t) on the interval…

A: Answer

Q: What value of a makes ƒ(x) = x2 + (a/x)have a local minimum at x = 2?

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

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Q: Find the absolute meximum and absolul-e minimum of fcx) = X intereval [4,8] x- 48X Over the

A: From the given function; fx=x33+x2-48x First, we have to find the critical points; As we know that,…

Q: 26 a. The function f(x)=x- 6x² + 9x-3 is defined on the interval [0,5]. Find the critical points of…

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: Find the absolute maximum and the absolute minimum of f(x,y)= 3xy-3x-6y+1 on the closed triangular…

A: Given:- The function is, f(x,y)=3xy-3x-6y+1on the closed triangular region whose vertices are (0,0),…

Q: 3) Find the abolute maximum and absolute minimum valuer of f(x) = x²-6x+5 %3D

A: using double derivative test

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

A: Given, function is

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: Find the local minimum value of f(, y) = 4+ x1 + yl – 11xy.

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Q: 5. Find the absolute maximum and absolute minimum values of f(x, y) = 3xy-3x– 6y+1 on the closed…

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Q: Let fx) = x + 2x-8. For what value(s) of x does fx) have a local minimum?

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Q: Find the critical point of the function, then determine if it is a local maximum, local minimum, or…

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