Consider the function f(x)=12x5+45x4−80x3+7  f(x) has inflection points at (reading from left to right) x = D, E, and F where D is and E is and F is

Q: Find the maximum and minimum value of f(x,y) =x3+3xy2-3x2-3y2+4

A: fx,y=x3+3xy2-3x2-3y2+4   fx=3x2+3y2-6x   fxx=6x-6   fxy=6y   fy=6xy-6y   fyy=6x-6

Q: Sketch the domain of the f(x, y) = ln((x² + x² – 4)(16 – x² – y²)) |

A: Recall:  Domain of the function:           The domain of the function is the set of all values for…

Q: Suppose that f(x) dx = 5. Calculate (4f(x) + 3) dæ-

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Q: The derivative of f(x) = Vx +2Vx 1 is A f'(x) = (2x + 1) Vx² – x – 2 2x2 – 2x – 4 B none of the…

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Q: d) Find the value of the constants ´ a ' and “ b ` that makes the function continuous at x=3 ; x3

A: f(x) is continuous at x = k if

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 linearization L(x) of the function f(x) = x^3/4 at x=256.  L(x)=?

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Q: Find the linearization of the function f(x) = x^8 at x = 1

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Q: given f(x)=x4-8x2+2, find all x-values such that f(x) has horizontal tangent lines

A: Compute the derivative of the given function.

Q: Let h(x) = f(z) where f(x) = ln(3x² + 2x +2) and g(x) = -2x. What is h' (x)?

A: hx=fxgx=ln3x2+2x+2-2xf(x)=ln3x2+2x+2 Differentiate f with respect to 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: If f'(x) = x³ – 2x* + x³ + 2, then f has inflection points at

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Q: Find the maximum and minimum values of the 2x3 function f(x,y) = * - 2xy – 5x + 2y² + 4y + – 2xy –…

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Q: find all critical points of the function. f (x) = x2 − 2x + 4

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Q: Find the critical numbers of the function. a. f(x) = x³ + 6x2 – 15x

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Q: Let h(x)=f(x)g(x). If f(x)=ln(3x2−2x−4) and g(x)=3x−1, what is h′(x)?

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Q: Find and classify the critical points of the function f (x, y) = 16x³ – 12x2 + 12xy? + 3y?

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Q: Find the local and absolute extremum for the functions over their domain: 5. f(x) = vx2 + 8x + 20

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Q: find the critical point and classify it. a. f (x,y) =xlny + x2 -4x -5y + 8

A: The answer is given below:

Q: Find the critical numbers of the function. (E F(x) = x4/5(x – 5)² %3D

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Q: The antiderivative of the function f(x) = -+ 1lx is x2 -5 + 5.5x2 + c -5 5.5x2 + c -11 + 2.5x2 + c +…

A: We know that, The expression to calculate the antiderivative of the given function: Fx=∫fxdx The…

Q: Find the Quadratic approximation of the function at the given value f(x) = 1n(x + 1)     near a = 0

A: Given  The function is f(x) = ln(x + 1)     near a = 0 .   Formula for Quadratic approximation :-…

Q: The function f(x) =x³ – 3x2 + 3x -1, x e R has a point of inflection | at A) x = 1 B) x =-1 C) x = 3…

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

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Q: Find the absolute extrema of the function on the closed interval.

A: Solution Given Find the derivative of the functionf'(x)=xx2+1To find the criticle Number derivative…

Q: Find the maximum and minimum values of f(x, y)=x+3xy2-3x2-3y²+4.

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

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Q: Use the linear approximation (1 + x)k = 1 + kx to find anapproximation for the function ƒ(x) for…

A: Given: ƒ(x) = (4 + 3x)1/3

Q: Find the critical point of the function f(x, y) = – 7 2x + 5x2 - 8y – 5y? |

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Q: Find the convolution of (a) Ila * IIa. (b) f(x) * f(x), where f(x) = e-l=l, -0 < x < o. %3D

A: Convolution : The convolution of two functions f(x) and g(x) is given by f(x)*g(x)=∫-∞∞f(y)g(x-y)dy…

Q: 4. Find the point on the graph of f(x) 5x2 + 20x – 3 where the tan gent line is horizontal. (a)…

A: We have to solve integration

Q: The function f(x) =x -x² – 2x – 1 is increasing over: %3D

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Q: Let h(x)=f(x)g(x), where f(x)=ln(4x2−3x) and g(x)=3x−1. What is h′(x)?

A: GIVEN,     f(x) =ln (4x2-3x)                  g(x)  = 3x-1                  h(x) = f(x) g(x)

Q: Let h(x)=f(x)/g(x), where f(x)=ln(3x2 +2x+2) and g(x)=−2x. What is h′(x)?

A: Here we use quotient rule, which is pq'=p'q-pq'q2

Q: let h(x) = f(x)/g(x), where f(x) = -3x^2 + 2x + 2 and g(x) = -2, what is h'(x)?

A: Given  hx=fxgxwherefx=-3x2+2x+2gx=-2 To find the derivative of h(x) Quotient rule is to be used…

Q: Find the global extrema of the function f(x)=x4−2x2−1 on [0,+∞).

A: Given function is Differentiating both sides with respect to x, we get Now, we will find critical…

Q: Find the extreme values of the function f(x; y) = x2 + y2 + xy on the curve x2 + 2y2 = 1.

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Q: Find the most general antiderivative of f(æ) = -5x + (1 – a²)-1/2, where -1 < x < 1. F(x) =

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Q: The function f(x) 223 42x? + 240x – 11 has two critical numbers. The smaller one is x = and the…

A: Let's find.

Q: What is the value of In[f'(2)]if f (x) = e*?

A: Our Aim is to tell the value of ln f'(2) if f(x)=ex-(i)

Q: Find the local extrema of the function f(x)=√x2+1.

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Q: Find the critical numbers of the function. a. f(x) = x3 + 6x? – 15x b. g(x) = V1- x2

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Q: The function f(x) = 2x + 6x² – 5x + 1 is concave downward on the interval None (-0, –1) (-0, c0)…

A: Concavity.

Q: 3- For what value of c is the function continuous? Provide a well- communicated solution. F(x) = {…

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Q: Compute f(x) and f(x) dx for the function f(x) = ∞  ∑…

A: f(x)=∑n=0∞x2n2n !.....(1)This is the well known series of the cosh(x)cosh(x)=∑n=0∞x2n2n !Now as we…

Q: If F(x) is an antiderivative of x2 + x1, then what is the value of F(1) - F(-1)? -2

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Q: find the maximum and minimum values of f(x,y)=x3+3xy2-3x2-3y2+4

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Q: What is the domain of the function f(x) = %3D 5" Vn n-1

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Q: Find the absolute maximum value of the function f(x) =-z² – 4x – 2 on the interval [3, 3 ]. a) О-2…

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Q: Find an antiderivative of ƒ(x) = 3x2 that satisfies F(1) = -1.

A: f(x)=3x2, F(1)=-1