Consider the following. if x s 2 S2 - x |x² – 4x + 4 f(x) = if x > 2 Is f differentiable at 2? O Yes O No Sketch the graph of f. y y 10 10 5 X - 10 -5 5 10 -10 -5 10 - 10 - 10 y y 10 - 10 -5 10 - 10 -5 5 10 - 5 - 10 Sketch the graph of f'. y y 10 10 5 X 40 10 40 5 10

Q: Consider the following function. 9(x) = x2/3 (a) If a + 0, find g'(a). g'(a) = (b) Illustrate that y…

A:

Q: A particle is moving along a line, whose directed distance from its origin is given by the function…

A: f(t) is a distance function.

Q: 7) Calculate the slopes of the following functions at the given points: Ta) f(x) = ln (x²-x + at IL)…

A:

Q: + [ƒ(2)₁ Suppose that fand gare continuous functions such that 1 [ g(x)dz -3, find f(x)dx= 2 and +…

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Q: 4. Find the extrema of the function f(x) = Vx (x + 1) and the intervals on which its graph is…

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Q: If f(x) = ∫0 x   (1 - t^2)e^t^2 dt , on what interval is f increasing?

A: To determine the interval on which f is increasing. f(x)=∫0x(1-t2)et2dt

Q: If we have that f: R → Ris a continuous function , in which f'(7) = 6 and f(7) = -2 an equation of…

A: We have to find out tangent line

Q: Find the points at which y=f(x)=x9−17xy=f(x)=x9−17x has a global maximum and minimum on the interval…

A: We find the critical points using f'(x)=0 -1.0827 is not in the interval [0,4]

Q: Q2: Find dyidx for the following function:- (1) y = In(x + 4)-xtan (4) y =x*+1) (2) xy + x*y = x +…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Consider the piecewise-defined function f defined by S 7– 2x? if x >1 f(x) = 19 – 4x if x < 1 Find…

A: This means f(x) is continuous at x=1

Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

A: Please see the answer below

Q: is concave up on interval The graph of f(x)= x2 – 1 OA(-1,1) OB (0,1) oC(-1.0) U (1, 00) OP (-x,-1)U…

A: F is concave up if f’’(x) &gt; 0.

Q: ind the critical points of the function f(x, y) = x² + y² + 10x – 9y + 3. List your answers as point…

A: In this question, concept of critical points is applied. Critical Points The critical points of a…

Q: Q4) The critical points of the function f(x, y) = 8y³ – 12xy + x³ O (0,0) and (1,2) O (0,0) and…

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Q: -2? + 15z - 27 f(z) = 3z2 + 7z + 6 C, I= 3 What value of C would make f(x) continuous at z = 3?

A:

Q: The slope of the tangent line to the graph of the function y=3V-4at (16,8) is 16.00 4. -1.00 O-0.50…

A: Now,

Q: ,is concave up on interval x2-1 The graph of f(x)D OA (-1,1) OB. (0,1) В. Oc. (-1,0) U (1, 0) OD.…

A:

Q: 4. Suppose that F(t) is a differentiable function of one variable. Define the function z(x, y) = e'F…

A: z(x,y) ey F (exy )diff wrt xdzdx = ey F' ex/ye.1/yzx = ey.ex/yyF' (ex/y)and diff wrt ydzdy= ey…

Q: dy 6. If y is a differentiable function of x and r + 2y3 x² = 8y?, then find dr

A: This question is based on diffrentiation chain rule.

Q: 9. Show the function f(z) = 1 + 2i+2Re(z) is differentiable or not differentiable at any points.

A: Solution

Q: 4). If f(1) = 12 and f' is continuous and | f'(x) dx=17, what is the value of f(4)?

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Q: For all but two choices of a, the function (x) x if x a will be discontinuous at the point x = a.…

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Q: | (r – 1)³ + 1, if x 2 1. Determine if g(x) = is differentiable at x = 2.

A: Checking continuity:=limx→2- g(x)=limx→2- (x-1)3+1  limx→2- g(x) =2Right hand side limit=limx→2+…

Q: 2 + 7x if x < 4 Let f(x) if x 2 4. For what value of the constant c is the function f continuous on…

A: Given function is: fx=cx2+7x       if x&lt;4x3-cx          if x≥4 We know that a function is…

Q: Find the marginal value such that function f given f(x) =x2+ax+1 is strictly increasing on (1,2)

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Q: If f(x) = In(tanh(2x)), then f' (x) is Select one: a. -2 coth(2x)sech (2x) :): b. – coth(2x)sech (2x…

A: f(x)=ln(tanh(2x))f'(x)= 1tanh(2x) ddxtanh(2x)we know that  tanhx=ex-e-xex+ e-x…

Q: x2 – 1, if x 1 Let f(x) (a) Is y = f(x) continuous at x = 1? (b) Is y = f(x) continuous at x = 2?

A:

Q: if x 0 f' _(0) f',(0) Is f differentiable at 0? Yes No

A: To find f is differentiable at 0 or not

Q: 1. Show that function f(x)=D|x | is not differentiable at 0

A: As per company guidelines we can solve first question. I hope that the given solution will help you.…

Q: 4). If f(1) = 12 and f' is continuous and f'(x) dx=17, what is the value of f(4)?

A:

Q: 3. Suppose that {f(t)} = F(s) with F a differentiable function and that L{f'(t)} Exists. Then…

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Q: Find f'_(0) and f'„(0) for the given function f. (If an answer does not exist, enter DNE.) if x 0…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: (c) Determine whether the following function continuous at point (0, 0). Justify your answer. 2–xy…

A:

Q: 5. Suppose the function g is defined by g(z) = { kz+1 for 0 < x< 3 for 3 <r < 5, mx + 2 where k and…

A: Given function is g(x)=kx+1  ,0≤x≤3mx+2 , 3&lt;x≤5 limx→3-f(x)=limx→3-kx+1=2k…

Q: Q3) If the function (2x + 1 +2 x > h) XSh f(x) having limit at x = h. Find the value of h. Q4) f(x,…

A: Our objective is to solve the above questions.

Q: if x1 O No, since g(x) is undefined at x=1. O Yes, and g'(1)=3. O Yes, and g'(1)=8. O No, since g(x)…

A: Given

Q: (Read the dėlihition Caleluny.) |x2, if x l; is differentiable at 1. 2x-1, ifx > I; 4. Prove that…

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Q: Sketch the graph of function f(x, v)- J4-x - and draw the level curves at k- 0, 1,4

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Q: Find minimum and maximum for the function 6 x + 4 y under conditions: x2 0; yz 0; -x+y s 12; x+ys…

A: The objective is to find maximum and minimum value of the function 6x+4y.

Q: 7. Suppose that the function f (x)=2-sin(e*) is continuous on with equal step 2'2 size, h equal to .…

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Q: Answer the following questions for the function f(x) = xVx² + 25 defined on the interval [-7,5].…

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Q: x², if xs1 4. Let f(x) = . Find f. (1) andf'(1). Does f'(1) exists? 2x, if x>1 Show that the…

A: 4. fx=x2,if x≤12x,if x&gt;15. y=f(x)=x2-3x

Q: Which of the following curves have critical points at x=2 and x=-2 * f(x) f(x) = 12 + 4x + 4 x2 – 4x…

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Q: Find the points at which y=f(x)=x^9−17x has a global maximum and minimum on the interval 0≤x≤4.…

A: To determine the global maximum and minimum.

Q: 1 if z 0. Is F(x) is continuous at I = 0? Justify your answer.

A: Given that for x&lt;=0, F(x) = (x - 1)/4 Then as x tends to zero from the negative side of zero, we…

Q: (b) Sketch the graph of a function that has a local maximum at 3 and is continuous but not…

A: To sketch the graph of the function which is local maxima at 3 and not differentiable at 3

Q: 以く2 g(x) = X = 2 *一2 h continuous at MArDl (0,2]

A: The given function is: g(x)=x2+1, x&lt;25        ,x=21x-2,x&gt;2