Given a function: f(x) = x⁴ + x³ − 2x² + 3, x ε ℝ Shows that: a. Find the extrema points. b. Shows that following statement is TRUE or FALSE: the f(x) domain will always on positive values, f(x) ε ℝ+.

Q: Given the function f(x) = x³ - 3x2 x – 1, determine all coordinate points (x, y) on the graph of f…

A: The derivative of the function will give the value of slope. For two value of x, f(x) will have…

Q: Consider the function f(x)=xe−9x,0≤x≤2. On this interval, ff has a minimum value equal to: which is…

A: Given fx=xe-9x 0≤x≤2

Q: Given 3y = x^3 + 3x^2 - 9x + 3, Find the relative extrema of f by applying the second-derivative…

A: Given ,  3y=x3+3x2-9x+3. Let y= f(x) Above equation can be written as     y=x33+x2-3x+1     or…

Q: Find the value k that makes the function continuous. (ka?, x > -2 f (x) kx + 18, x < -2

A:

Q: 7. For the function f (x)=(x-2)° +1, a. Sketch the graph of over the interval [0,3].

A:

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A: The given function is

Q: 12. For the function f(x) = x² + 10x + 7, x ER, find any global maxima or minima points

A: If y=f(x), then the independent variable x is called the input of the function and the dependent…

Q: For the function f(x)=x3-3x, its local maximum is which occurs at ( its local minimum is which…

A:

Q: If f is a differentiable function and such that and g(x) = x+2 / 1+f(x) such that f(0) = -2 and…

A: Given: gx=x+21+fx f0=-2 and f'0=5 We have to find the value of g'0.

Q: The function h(x)=1/x−4, can be expressed in the form f(g(x)), where g(x)=(x−4), and f(x) is defined…

A: Given: ------------------------------------------------------------------------------------------…

Q: Find the value of constant K that makes the function below continuous at x = 2. -2x X < 2 X-2 f(x)…

A: Given,           fx=x2-2xx-2 ; x&lt;2kx-3 ; x≥2

Q: If the critical point of the function f(x.y)-x- y- 2xy +6 is (0.0). test this point whether it is:

A: We use second order partial derivative to know about critical point behaviour

Q: For the function f(x)=x^3−27x, its local maximum is __ which occurs at (___; its local minimum is __…

A: To find the local maximum and local minimum for the function f(x) = x3 – 27x

Q: Given f(x) = x^3 - 27x + 5, list the interval (a,b) where f(x) is decreasing, AND at what x-value…

A:

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: Find the absolute extrema of the function f(x)= (x^3)-(9/2)(x^2)-30x+3 on the interval [0,6]

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Q: Find the absolute maximum and minimum of the function f (x) = x³ - x+2 on the interval [0, 3] %D

A:

Q: Given the function f(x) =4x³– 39x²+90x +2, which of the following describes its absolute extrema at…

A: Given that, The function is following, f(x) = 4x3 - 39x2 + 90x + 2 We have to find the absolute…

Q: b. For what value of (k) is the function y=f(x) continuous at x=3. x3-3x2-4x+12 x#3 x-3 f(x) = k x =…

A:

Q: Find the value of a that makes the following function differentiablefor all x-values

A:

Q: Find the maximum and minimum values of the function f(x) = x² – 6.x +7 on the interval [0, 5].

A: It is given that, f(x)=x2-6x+7   , on the interval 0,5We have to find the maximum and minimum values…

Q: At which r-values is the following function g differentiable? Explain and compute, where necessary.…

A:

Q: Find k such that the line is tangent to the graph of the function.…

A: To Determine: Find k such that the line is tangent to the graph of the function.…

Q: 2 For the function f(x) = -x', find f'"(x), f'"(0), f'"(1), and f"(- 1).

A: To find the double derivative for the given function.

Q: Find the value of k so that the function 5x+3 if x<3 f(x) =. kx2 if x 23 is continuous everywhere?

A:

Q: For the function f(x), defined graphically, state the value(s) of x where the function is not…

A:

Q: On what interval(s) is the function f(x) = x* – 4.x³ both decreasing and - up? concave A

A:

Q: Over the interval (0,2), the function f(x) = (-x²) e*

A:

Q: For what value of c is the function f(x) = = C= C 7 2-4 (x+2)(x-3) x==2 x = 1 otherwise continuous…

A: Given :fx=c,      x=-27,        x=1x2-4x+2x-3   otherwise

Q: Consider the function f(x) = - 2x + 24x2 42x +4. %3D - Find the critical points.

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

A:

Q: the

A: We will find the local minima, maxima, and inflection points.

Q: For what value of x does the function f(x) = x - 3x attain the absolute maximum in the interval…

A: The solution is given as follows

Q: For what value of x does the function f(x) 4x attain the absolute minimum = in the interval [-3,5]?…

A:

Q: show steps please.

A: We will find the first two derivatives of F(x) We use the fundamental theorem of calculus To find…

Q: Consider the function f(x,y) - x-44x- 4y and determine if, at the point (4,0) if the function is a…

A: Note: Since you asked multiple questions I solved one. For solution of other problem please post the…

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: Given:-f(x)=3+3x-3x2 ; 0, 3f'(x)=3-6xfor critical pointsf'(x)=03-6x=06x=3x=36=12second derivative…

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A:

Q: What is the value for k if f(x) =x² + kr + 13 is an even function?

A:

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

A:

Q: If f (x) - 2x - kex has a relative maximum at x = -2, then the value of his

A: Given  f(x)=2x-k.exNote: As there is no h in the equation it is assumed that we need to find…

Q: (b) For what values of the constants c and d is the function continuous and differentiable for all…

A:

Q: At x = 3, the function given by f(x)={x2 , x<3 and 6x−9, x≧3 is? a) undefined b) continuous but…

A: Given function: fx=x2x&lt;36x-9x≥3 Clearly the function is defined on all real numbers. We have to…

Q: Find the absolute maximum and minimum values of f in the given interval. f(x) = x* – 2x² + 1, (-2,…

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Q: Find the lineearization L(x) of the function f(x) = x^3/4 at x = 16.

A:

Q: Find the value for k so that the function will be continuous at x = 2. 4x2 – 12x + 8 6 if x 2

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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: Find a value for the constant k, if possible, that will make the function continuous. kox+1 for x 3

A: K = 1/3

Q: For the following function, find appropriate function g(x) of fixed point method: f (x) = xe* – 1 -

A: g(x)=