Suppose we know that f(x) is continuous and differentiable on the interval [-7,0], that f(-7) = -3 and that f'(x) < 2. What is the largest possible value for f (0)?

Q: We note that F is continuous for all x, and its derivative is (x-1) if x>0 F'(x)= -1 if xr<0 The…

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Q: The absolute minimum value of the function f(x) = –3 sinx on the interval [2, 8] is

A: To find the absolute minimum value of f(x), first we have to find the derivative of f(x) i.e. f'(x).…

Q: Give an example showing that, even if f 0 (c) = 0, it could happen that f(x) does not have a local…

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Q: find all critical points of the function f (x) = sin^−1 x − 2x

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Q: Suppose f is continuous on an interval containing a critical point c and f 1c2 = 0. How do you…

A: The critical point of  f is x=c and f'c=0.

Q: The tangent line to y=f(x)y=f(x) at (−3,−2)(−3,−2) passes through the point (−4,−3)(−4,−3). Compute…

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Q: What is the critical point of the function f (x) = cos x?

A: what is the critical point of f(x)=cos(x)? for critical point, f'(x)=0

Q: тт Find the absolute minimum and maximum of f(x) = 2 sec x tan x on the interval [-- 4' 4

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Q: Use the first derivatives test to find local exterma of f( x) =x3 -12x on R

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Q: Suppose that the FIRST DERIVATIVE of a function f is given by f' (x) = (x – 3)² (z² + 5x). Find the…

A: We find the critical numbers by solving f'(x)=0

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x ln…

A: Now differentiating with respect to x, we get

Q: Find the points of local minimum and  local  maximum of the functions f(x) = sin2x where x belongs…

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Q: The critical numbers z = 1 and x = -2 are found from a continuous function f' (z). Given that the…

A: The Solution is given below

Q: 10. f(x) = cos (2x)e*²-1

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Q: find all critical points of the function f (x) = x ln x

A: Given: First, take the derivative equals to zero. Therefore,

Q: Find the critical numbers for function f(x)=x-3 ln(x)

A: Given function:  fx=x-3lnx

Q: 2) Let f(x) = x' +x² – 5x – 5. Use the second derivative test to classify the critical points.

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Q: Find the critical coordinates of f(x) = x³ – 3x² + 8x + 1. Then, distinguish the local maximum and…

A: Given function is  f(x) = 13x3-3x2+8x+1                 ....(1) Differentiate with respect to x , we…

Q: find the critical points of f (x) and use the Second Derivative Test (if possible) to determine…

A: Here we will apply first derivative and equate it to 0 to get the critical points and then apply…

Q: Why does the maximum and minimum points for y = f (x) occur among the minimum and maximum points for…

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Q: Find all critical points of the function: f (x) = sec−1 x − ln x

A: Given function f(x) = sec−1 x − ln x

Q: Find the weak derivative of f() = |x² – x + 1/5| on the 1) interval (0,1).

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Q: Assuming that the derivative of arcsin(x) is indeed 1/√1 − x2, supply the justification that allows…

A: Recall the power series expansion for 1/√(1 − x2) The same  can be written as: 1/√(1 − x2) = c0 +…

Q: 10. Show that f (x) = { x² sin(1/x) if x + 0 if x is differentiable, but the derivative is not…

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Q: the value of x at which the FOC is satisfied give us the ........(maximum/minimum) of the function…

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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)

Q: Find the critical points and the intervals on which the function f(x) = (x³ - x) e* + 4 is…

A: To find out critical values, take derivative, apply product rule

Q: Find the critical points of the function x + 1 f (x) = (5 – x)² -

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Q: Find the value of K that make the function f continuous at x=2 -4 スー3x+2 sin(nx) + kx + k if x 2

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Q: For a function f (x, y), (0, 0) and (1, 1) are two critical points. Also, fxx = 2x², fyy = y²2 and…

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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: On the graph of f(x)=sinx and the interval [−2π,0), for what value of x does f(x) achieve a minimum?

A: The given function is fx=sinx Differentiating w.r.t. x to both sides- f'x=cosx To find the critical…

Q: Find the critical point and the interval on which the given function is increasing or decreasing,…

A: The given function is fx=9x2+7. Note that, the denominator of the above function is not 0 for any…

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

Q: Suppose the derivative of a function is x2 + 2x -3. a) On which open interval/s is the function…

A: Consider the given: Given:f'x=x2+2x-3 Find the critical numbers: Substitute…

Q: Suppose f is continuous on an interval containing a critical point c and f"(c) = 0. How do you…

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Q: Suppose (1,1) is a critical point of a function f with continuous second derivatives. In each case,…

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Q: let  f(x)=  x+2  if x1 Find the value of k that will make f continuous on (-∞,∞)

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Q: Consider the function f(x) = -2x² + 8x – 9. f(x) is increasing on the interval (-o, A] and…

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Q: The tangent line to y=f(x) at (−8,−5) passes through the point (−3,10). Compute the following f(-8)…

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Q: 4. By the definition of derivative prove that f(x) = √x² +5 is differen- tiable at x=2.

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Q: The coordinates of the critical point according to the criterion of the first derivative of the…

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Q: Suppose f is continuous on an interval containing a critical pointc and f″(c) = 0. How do you…

A: According to the second derivative test, If c= critical value. if f''(c)&lt;0, then f(x) has local…

Q: Find the first derivative: In 2x f (x) 1- In 2x f(x) = In (sec x) f(x) = cos (In x) f(x) = In[cos…

A: we can answer only three subparts, or the first question and the rest can be reposted. No more than…

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: 3 Find the derivative with gicapeet to X If f(0 = 0-7 The derivatie with reapeet to X If -7X is…

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Q: Suppose that a function f(x,y) has a critical point at (2,3). Given that fæx (2, 3) = -4, fæy(2,3) =…

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Q: The stock price for a certain corporation can be approximated for the years 2012 through 2017 by…

A: Given that                                                         f(x)=6.3x2-168x+1199 derivative…

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: