d the local max and min values of the function f(x)= 3x3 – 2x if it exists.

Q: The function f(x) = 11 – 7x has an absolute maximum value of and this occurs at x equals

A:

Q: If c is a non zero constant then the function is always differentiable x2 + c2

A:

Q: Find the linear approximation to f(x)=x2+1x−2 near a=3.

A: Given: f(x) = x2 +1x − 2; a = 3

Q: Find the formula for a function of the form y=be^((-(x-a)^2)/2) with its maximum at the point (0,5).…

A:

Q: b) Find the absolute maximum and minimum values of function f(x) = (x– 2)5 over the interval [-3, 4]

A: Absolute extrema can occur either at the points of local extrema or the boundaries of the interval.…

Q: Find the linearization of the function at a . f(x) = x 4 + 3 x2    , a = -1

A: We know that ,The linearization of the function at v=ais given by fa+f'ax-a

Q: Find the interval/s where the function is increasing and where it is decreasing: f (x) = x³ – 3x + 3…

A:

Q: 2 Z= 22,

A: Given  z=2x12+x1x2+4x22+x1x3+x32+2

Q: Find f′(x) and f′(c). Function f(x) = (2x2 − 3x)(9x + 4) Value of c = −1

A: f(x) = (2x2 − 3x)(9x + 4) c = −1   f'(x) = (2x2 − 3x).(9x + 4)' +  (2x2 − 3x)'. (9x + 4)        =…

Q: Find the absolute maximum and absolute minimum values of the function: f(x)=5x^7−7x^5−7 on the…

A: We find the critical points by solving f'(x)=0 Use power rule to find f'(x)

Q: The function f(x) = 2x3 – 39x? + 240x + 9 has derivative f'(x) = 6x? – 78x + 240. %3D f(x) has one…

A: Given data:   The expression for the given function is f(x)=2x3-39x2+240x+9. The expression for the…

Q: x²–1 If f(x) and g(x) = Vx – 1, which will yield (f 0 g)(x)? %3D r2

A:

Q: The function f(x)=x2 is decreasing on the interval...................... .

A: Given,f(x)=x2 f(x)=x2 On differentiating both sides w.r.t x we get: f'(x)=ddx(x2)⇒f'(x)=2x Now, we…

Q: The linear functions m(x) and n(x) are perpendicular to each other and intersect on the x-axis. If…

A: Two lines with slope m1 and m2 are perpendicular to each other if m1m2=-1 Given: m(x)=4x+48 Let the…

Q: Find the net change in the value of the function between the given inputs. f(x) = 3x - 2; from 1 to…

A: f(x)=3x-2now we have to find the net change in the value of function from 1 to…

Q: 1. Given the function f(x) = Vx5 – 3Vx², find the interval(s) of increase.

A:

Q: d) Find the value of the constants ' a’ and b ’ that makes the function continuous at x= 3 ах + b ;…

A:

Q: 1. Come up with the equation of any function f (x, y) satisfying fx = x + y and fy = x + 3y³

A: The objective is to find the function f(x,y) satisfying fx=x+y and fy=x+3y3 Now take, fx=x+y Now…

Q: 1 Find the linearization of the function f(x) = 5x+4 atz-1.

A: The given function fx=15x+4 at x=-1

Q: The function f(x) = 12 – 6x* has an absolute maximum value of 0 and this occurs at æ equals

A:

Q: 11b. Consider the function f(x)=5x* – 4x³ +4. Isƒconcave up or down at the point x = -0.2? A.

A:

Q: Find the local maxima and local minimum value of function f(x) =xx

A: We use first derivative test to find local maximum and minimum

Q: The function f(x) = x²e*- ex has a root in [0,2]

A:

Q: (a) f(x) = 2r3(3 – 4x)

A:

Q: Find the linearization of the function at x = 1.* f (x) 2x - 3x + 7 %3D

A: From the given problem:   fx=2x3-3x+7 ; x=1   As we know that the expression for linear…

Q: Find the positive critical point of the function f (x) %3D x4 + 7 x =

A:

Q: Q. 4 Find the absolute maximum and minimum values of f(x) = x³ + 5x2 – 7x over the closed interval…

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Q: Find the range of f(x)=x-5x+6. O [-1/4, 0)

A: The given function is:fx=x2-5x+6To find the range

Q: The profit function of a company is P(x) = x² – 400x + 40000, then the break-even poi is %3D

A: The break-even point point occurs when the total revenue is equal to the cost. At that point, the…

Q: 3- Show that the function y = x3 + 3x + 3 satisfy the y" + xy" 2y 0

A: Function does not satisfy the given inequality. See the attachment

Q: 3- Show that the function y = x³ + 3x + 3 satisfy the y= + xy= - 2y = 0

A:

Q: b) Find all points of local maxima and local minima of the function f(x) = x' – 3x + 3.

A: We use application of derivatives to solve this problem.

Q: DERIVE THE F. FUNCTIONS: s) y (x-3)(3x+4)(x²-2x+ 1)

A:

Q: given the function f(x)=axln(x+b), where function is decreasing at x=1-b?

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Q: The interval in which the given function is decreasing is at y = x3 – x2 – 5x – 4

A:

Q: (c) Show that max p(x) —D А X#0 min p(x) = and %3D X#0

A: It is defined that ρx=Ax,xx,x To prove part c) Let A be a Hermitian matrix. And λ1,λ2,...λn be eigen…

Q: Find the Critical number of the function f(x) = -2x^2 + 16x + 7. x = ?

A:

Q: Find a and b so that the function 2.3 – 5x² + 2, x -2 f(x) = ax + b, is both continuous and…

A:

Q: Q.20 For the function f(x) = x2 ex, the maximum occurs when x is equal to

A: Introduction :

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

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Q: The linear function f(x) = ax + b is a constant function if?

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Q: 7. Find f'(x) for the function f (x) = V-3x4 – 2

A:

Q: Find the absolute maximum value of the function. f(x) = 2(x – e*)

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Q: Find the global extrema of the function f(x)=3x4−6x2+2 on the interval [−2,2]

A: Global extrema of a function exists at critical points or at the end points of the interval.…

Q: Find the x-values of the stationary points of the function  f(x) = x^4 + 4x^3 - 4x^2 - 24x

A: Given: f(x)=x4+4x3−4x2−24x

Q: 3. Given the function g(x) = x - 2x2 + x, find the interval(s) when g is concave up and decreasing…

A: We have given a function g(x).  We have to find the interval where g is concave up and decreasing at…

Q: B4: a) Find and classify all critical points of the function f(x) = x³ + 3x² – 12x + 5

A: In the question we have to find critical points.

Q: The function f(x) = 12 – 6x4 has an absolute maximum value of and this occurs at x equals

A: