Let A be a positive real number. If the absolute minimum value of f(x) = Ax³ – 90x³ on [0, 00) occurs at a = VcAk then find c.

Q: Find the values of constants a, b, and c so that the graph ofy = ax3 + bx2 + cx has a local maximum…

A: Given that: y = ax3 + bx2 + cx has a local maximum at x = 3, local minimum at x = -1, and inflection…

Q: find a so that f (x) = ax2 + 8x -8 has a minimum value of -24

A: According to the given information, it is required to find the value of a so, that the function f(x)…

Q: find the max im um anel minimum Limits of the functibu n Fix.y) = x"+y"-2x²- 4xy- 2y²

A: The given function is F(x,y)=x4+y4-2x2-4xy-2y2    …..(1) Differentiating partially with respect to x…

Q: ded on the y-axi

A: In this question, the concept of maxima and minima is applied. Maxima and Minima The extrema of a…

Q: Let f:R where R be defined f(x) =4x2-4x+11 .Find the global minimum value and a point of global…

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

Q: If  f has a local minimum value at , show that the function g(x)  =-f(x)has a local maximum value at…

A: Let  g(x)=-f(x) g'(x)=-f'(x) If f(x) is increasing in interval (a,b) , then  That is if f(x) is…

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

A:

Q: Find the absolute minimum and absolute maximum values of fon the given interval. Rx) = x- In(7x), 2…

A: The given function is fx=x-ln7x,  12,2.

Q: Provide an appropriate response. Given that x > 0, find the maximum value, if any, of x-x".

A: Given that x>0. We have to find the maximum value of  x1x5.

Q: find the points at which f has a local maximum or a local minimum

A: This question can be solved using the concept of maxima and minima.

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: Prove that the function f(x)  =x101  + x51  +x  +1 hasneither a local maximum nor a local minimum.

A:

Q: Find the absolute maximum and absolute minimumvalues of f on the given interval.   f(x) =5 +54x  -…

A: Absolute maximum or absolute minimum values of a function on the given interval exists at a point at…

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

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

Q: Find the absolute maximum and absolute minimum values of z€

A: This question can be solved using the concept of absolute maximum and absolute minimum.

Q: Identify the absolute minimum of p(x)=−x2 −1 over [−1,5].

A: Find the absolute minimum of the function on given interval.First find the derivative of the given…

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

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

A:

Q: Let A be a positive real number. If the absolute minimum value of f(z) = Ar- 20x on [0, o0) occurs…

A: Given that  The absolute minimum value of f(x) occurs at x=sqrt(cA^k)

Q: Let f (x) be the square of the distance from the point (2, 1) to a point (x, 3x + 2) on the line y =…

A: The square of the distance between two points (a, b) and (c, d) = (c - a)2 + (d - b)2

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: Let A be a positive real number. If the absolute minimum value of 60x on 0, oo) occurs at a = f(x) =…

A:

Q: A be a positive real number. If the absolute minimum value of f(x)= Ax³ – 45x³ on [0, ∞) occurs at x…

A: Applying critical point and absolute value test

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

A:

Q: f(x)D has a absolute minimum on [1,3] of 1/319 1/x

A:

Q: If f has a local minimum at x = 0 and a local maximum at x = 2, what can you say about f'(0) and…

A:

Q: Let f(x) = 4x – 8a2 + 5x. Find the absolute maximum and the absolute minimum of f on [0, 2].

A: To find  The absolute maximum and absolute minimum of f(x) at [0, 2]

Q: Let C be a real number and let f(x) = - - 6C. If the slope of the tangent 3 2 line to the graph of…

A: Given : f(x) = Cx33-6Cx22 Slope = -108 at point of inflection

Q: Find the absolute maximum and absolute minimumvalues of  f on the given interval.

A:

Q: Let a, B be positive numbers. Find the absolute maximum value of f(x) = x°(1 – x)*, 0 < x < 1.

A: To find the absolute maximum of the given function.

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

A: Answer

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

A:

Q: Find the absolute minimum value of the function f(x) = et (0, 0). on

A: Given function f(x) = exx    on   0 , ∞

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: Please

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

A: using double derivative test

Q: The absolute minimum value of the function f(T) = 3x2 - 6x +4 over the interval [0,4] %3D O 1 O 5 O…

A: Equate the derivative of the function to zero and solve for x .

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

A:

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: (b) Estimate the value of x at whichf has a relative maximum. If there is no relative maximum, enter…

A:

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

A:

Q: Find a cubic function f(x)=ax^3-bx^2+cx-d that has a local maximum value of 112 at 1 and a local…

A: Find a cubic function f(x)=ax^3-bx^2+cx-d that has a local maximum value of 112 at 1 and a local…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.