Sketch the grTaph of a function f that satisfies all of the given conditions (@) /(-1) = 4, f(1) = -2, and f(3) = 1, (b) S(-1) – f(1) = /(3) = 0, (c) f'(r) > 0 ife< -1 or 1 < r<3, (d) S(r) < 0 if -1 < r , , 1 or (e) /"(r) > 0 if 0 2

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A: Apply Limit rule

Q: ) The tangent line to y = f(x) at (-5, 2) passes through the point (-7, -5). Compute the following.…

A:

Q: : Verify Mean value theorem for the function f(z) = 4x over the interval [0, 2].

A: As given function is: fx=4x3 Given interval is: 0,2 According to mean value theorem for a continuous…

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Q: Find the derivative of g(x) = e * x). sin (1+ 0-3x²e*cos(1+x°) O xe*1sin(1+x°)+3x²e*cos(1+x) O…

A: The product rule of derivatives states that duv=u'v+v'u.

Q: 3. Is the function given by x²-4x-5 -,x< 5 f(x) =. x-5 x+1, x 2 5 continuous atx=5? Why or why not?

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Q: Find the local maximum and minimum values of f using the Second Derivative Test. If the Second…

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Q: Compute the derivative of f(x) = ( sin(2x + 1))/°. 4 (sin(2x+ 3 1) -1/3 • cos (2x + 1) 4 -1/3…

A: Given

Q: Please help. *Find the equation of the normal line (NL) to the graph f(x)=x³-4x at x = 3. *For…

A: To find the equation of normal line to the curve

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A: Here we have to determine whether the given function is continuous or not.

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A: The given function is f(x)=4x2We have to find the derivative of f(x).

Q: Show that given functions are orthogonal on the indicated interval. f1(x) = ex,   f2(x)= xe-x - e-x…

A: given functions are orthogonal on the i interval [0,2] are f1(x) = ex,   f2(x)= xe-x - e-x .

Q: The tangent line to y = f(x) at (-1,-8) passes through the point (-7,5). Compute the following a.)…

A: The tangent line to y=f(x) at (-1,-8) passes through the point (-7,5)

Q: 2 Find the derivative of f(x) =x² – 6 from limit definition. - Show all steps of working. f(x) :…

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Q: Consider Mean Value theorem for derivative for function f(x) 4(1-2x) in interval [0,1]. TCOS(TX) -

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Q: Use second derivative test, If f(x) = - 4x + 10 then f(x) has a local maximum at the point 3 %3D O r…

A: here we need to find the point at which the function has a local maxima. the solution is following.

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Q: How must f(0) be determined so that the function f(x) = x2-x ニー x0, is continuous x-1 at X= 0?

A: Let f be a real function . Let a be any point in its domain . If limx→afx exist and equal to fa Then…

Q: 9. Is the function defined by gon3 – 3 if 2. continuous at r= 2? differentiable at x = 2?

A:

Q: Find all x values in interval [0,2 ·¤] on the graph of f(x) = -3·sin(x)·cos(x) where the tangent…

A: Given,            f(x) = -3 sin(x) cos(x)

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Q: Suppose (-8, 6) is a critical point of a function f with continuous second derivatives. If fra (-8,…

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Q: A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f, the tangent…

A: Given problem:- A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f,…

Q: Find the derivative of f (x) = arcsin (x²). 2x f' (x) = 1-a4 f' (x) V1-x4 2x O f' (x) = V1-a² O f'…

A: Use differentiation of trigonometric function

Q: 3. ƒ : R+ → R, such that f(x) = √2x+2. (Hint: Apply the chain rule.)

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Q: Find local maximum or local minimum of f (x)=sin 2x-x defined on 2 2

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Q: Find the hundredth derivative of the function f (x) = cos(2x) . O f(100) (x) = -2100 cos(2x) O…

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Q: The derivative of the function f (x) = 3 sin“ x is Select one: O f'(x) = 12 cos³x O f'(x) = 12 sin³…

A: dsinxdx = cosx

Q: 4. Show that the function is continuous on (-00, 0). f(2) = {0 x* sin(1/x) if x 01 if x = 0 S

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Q: Find the critical numbers of the function  f(x) = 4x - tan x

A: fx=4x-tanx Differentiating with respect to x, we get f'x=41-sec2x=4-sec2x

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Q: Find sixth order derivative of the function f(x) = (x – 5)7.cos(5x) by using %3D Leibnitz theorem.

A: If y=uv where, u and v are functions of x then un and vn denote the nth derivative of u and v with…

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Q: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…

A: On solving this we will get

Q: The function f(x) whose derivative is sin x and whose graph passes through the point(0, 2)​

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Q: 1. Use the first derivative test to find the location of all local extrema for 3 f(x) = -x³ +x+ 18x…

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

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Q: It is defined as the limit of the ratio of the change in a function to the corresponding change in…

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Q: 5)Let f ( x ) =3x4 + 4x3 Find the derivative. b)Find the critical numbers.

A: Given problem:- 5)Let f ( x ) =3x4 + 4x3   a) Find the derivative.   b) Find the critical numbers.

Q: Find the function f(x) whose derivatives is sin x and whose graph passes through the point (0,2).…

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