10. f(x) = 2x3 – 9x² + 12x – 3 - -

Q: Analyze the critical points of f (x) = (2x − x2)ex .

A: fx=2x-x2ex Differentiating with respect to x, we get…

Q: 7) Suppose y varies directly with x. If y=2 when x = – - what is y when 2 X--0.3?

A: Given the data :

Q: 4. Calculate(Y/X)- – 2)* if: X = (; -) Y = (% ) z = ( ) (G Đ=z (F- )=« (4- )-

A: We will find out the required value.

Q: Find the critical points of the function f(x)=2x^2−4x.

A:

Q: are

A: We will find the critical points.

Q: メ Find dy S-3xメ+)X-2) (x211) (2X+3)

A: We have to find the derivative of y

Q: #! Find f'cx) if fex)= Čx²+SX+2)(X-)

A:

Q: find the extrema of f(x) =2x3-6x on [0,3]

A: Given:

Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+C₁e-ax using 2…

A:

Q: How do I show that F(x) are antidervatives of f(x)?

A:

Q: on of y" – 2y' + 2y =

A:

Q: 8. Show that y = x° + 3x +1 satisfies y" + xy" – 2y' = 0.

A:

Q: The ABC Company has determined that the cost of producing x widgets per weeks is C = f (x)= 2000 +…

A: C=fx=2000+100x-0.1x2 To find the cost of producing 100 widgets, put x=100 in cost function. That is,…

Q: X = (1-_-_-_-)* 2 o then f(x) tend:

A:

Q: Max Z = 4X1+10X2 %3D s.t. 5X1+4X2 < 200 X1+2X2 s 50 X1+X2 s 20 X1, X2 0

A:

Q: Show that Inx dx = -/Zn². x3/4(1+ x)

A: The given integral is: ∫0∞lnxx341+xdx

Q: 1. Find the critical points for f(x) = 3x5 – 20x3.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using 2…

A:

Q: b) y = In(xeVx + 2)

A: The solution are next step..

Q: If I have f^-1(x)= -x+1 how can I find f(x)?

A:

Q: y = v1- x+ x2 ||

A:

Q: [4] 2. Find f'(x) using the limit definition of the derivative. Credit will not be given for any…

A:

Q: 7 dy if Xy+2x +3y =1

A: We use implicit differentiate method to find dy/dx.

Q: How many critical points does the function f(x)=∣∣x3−12x∣∣ have?

A:

Q: 2) Find all relative extrema of ƒ(x)= x* – 4x³

A: Answer

Q: 2 The Range (Ry) of y = v9 – x² -

A:

Q: 1 If f(x, у, 2)- ôf then х— у—3z ду а. 1 (х- у-3-)2 b. -1 (х-у-3-)* С. 1 (х-у-3-)° d. 2 (х - у-3-)?

A: In Partial differentiation w.r.t y we treat x,z as constants.

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

A: y = 3x2/3 − 2x,                                   [−1, 1]   absolute extrema of the function = ?…

Q: Show two ways to differentiate ƒ(x) =

A: The function f(x)=1x10. We have to differentiate this function.

Q: Find the positive critical point of the function f (x) = x / x^4 + 4

A:

Q: 3 If y=/xL5x²_36 x²_3x²+Yx-12 (3 14 shuw that dy 24 dx4

A: firstly simplifying these expressions then , use the concept of differentiation

Q: 4.x +1 1 with f'(x) = 1/ 56x2 - 156x + 115 14x – 19 - - 3. Let f(r) = and f"(x) 4 %3D 3 5 Vr2 – 3x +…

A: To find the points on which it is concave up or concave down

Q: the first dirivative of f(x) =( 5x4 - 6x)-3 will be _______

A: Given : f(x) = (5x4 - 6x)–3

Q: Find the critical numbers of the function f(x) = 12x5 Round your answers to three decimal places.…

A: the given function is fx=12x5-45x4-40x3+2

Q: Find f(t). 2s + 3 s2 + 4s + 13,

A:

Q: 32. In y = 2y² - x; (2, 1)

A:

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

A:

Q: Suppose for a company that produces x amount of articles, the function of the marginal cost is given…

A: Given that   C'(X)=15x^2 -360x + 3510

Q: + 2x if xs -1 if -1 1 f(-4), f(-}). (-1), f(0), f(25)

A:

Q: Find all local extrema of f (x) = 4x3 – 3x² – 6x + 7 - -

A:

Q: Suppose z – 2z +x=5, What is the value of y ?

A:

Q: 4. Suppose y = 3x + 2. What is Ay if x increases by 3?

A:

Q: 8(x) = X -x3 + 2x x4

A:

Q: In a certain company, the income from the sale of x thousand pieces of products is given by I (x) =…

A: We first try to find the profit function.  Profit= Income - Cost…

Q: Differentiate x²y3 - y2-6x=0 with respect tox. A 3x²y2-2y −6+2ху 3 2х3у2-2y - 6 6-2xy3 3ху2+у В С D…

A:

Q: find the marginal revenue of the function. Using the quotient rule.  40x^2 -20x/x^2-10-2

A: Given: Revenue FunctionRx=40x2-20xx2-10-2 To Find: Marginal Revenue Concept: a. Marginal RevenueMx…

Q: 3 18. z= 19. y= Vx(x-1) 3x-1 20. y= 2x+1

A:

Q: find the critical valves of f(x)= 3x?

A: We can find the critical values as below.

Q: inh´x + cosh²x = 1 = x²arccsch(x²) then f

A: 1. The function fx=y=coshx is represented as , coshx=ex+e-x2 To check whether the function is odd…