Suppose we know that f(x) is continuous and differentiable on the interval [1, 9], that f(9) = 0 and that f'(x) > 8. What is the largest possible value of f(1)?

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: Suppose (1,1) is a critical point of a function f with continuous second derivatives and fz = 44,…

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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: Suppose that a PDF for a continuous variable X is given by if 0 x)=3/4

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Q: Suppose that Xis a continuous unknown with -4< X< 4  having PDF denoted fsatisfying f ( x ) = c (…

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Q: As the denominator df goes down, the critical value of F goes ______ so that  ______ extreme value…

A: ANOVA(Analysis of variance ) is an extension of the t-distribution. When we cannot use t…

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: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x - 1) + 2* -x has a critical number…

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Q: 2. Calculate the first derivative of f using the forward and backward difference approach in the…

A: The objective is to calculate the first derivative of f using the forward and backward difference…

Q: The stock price for a certain corporation can be approximated for the years 2009 through 2015 by…

A: In this question we are given with the function and we have to find the minimum stock price which we…

Q: Find the global maximum and minimum of the function on the given…

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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: Consider the following information fz(x, y) = 2xy - 2r³ and f₁(x, y) = x² + y² – 6. Use the Second…

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Q: 1. Show that a frination fiłamb ]->1R is differentiable at xolamb) is and only if its lower and…

A: Solution: f:[a,b]→ℝ is differentiable at x0(a,b). Let us take upper derivative at x0+. Then,…

Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x - 1) + 2* – x has a critical number…

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Q: 3. Use Rolle's Theorem to show that the function f (x) = x² sin(x) – x sin(x) has a critical point…

A: For y = f(x). Let f(x) is continuous at every point of the closed interval [a, b] and differentiable…

Q: To investigate these values, we find the second derivative f"(x) = %3D At the positive critical…

A: Given function is : fx=3x-4x3

Q: Since f'(x) > 0 when x 0 (x 1), f is increasing on the intervals (--, -1) and and decreasing on the…

A: Given that: f'(x)=-4x(x+1)2(x-1)2

Q: 8) Find the linearization of f(x) = 6 + X+1 tan 4 dt at x = 0. 1.

A: On solving this we will get

Q: Suppose that a firm uses L as an input, and its production function changes with L and a parameter…

A: Let’s apply the above approach to an economic application, namely the profit function of a…

Q: Consider the function ƒ(x) = x3. Where is the critical pointof ƒ? Does ƒ have a local maximum or…

A: Given  ƒ(x) = x3

Q: If f(x) is odd function, then the derivative of y=sinh (f (-x)) equals Select one: o y'=Xf'x) – f x)…

A: Differentiate wrt x

Q: 16. Show that f(x) = Vx - 2 is continuous at x=2 but not differentiable at x=2.

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Q: 2. Determine the second derivative of f(x) = x²e²* at x = -2 with a step-size of h=0.50 using…

A: Given function f(x)=x2e2x. The objective is to determine the second derivative of fx at x=-2 with a…

Q: Suppose /has a continuous derivative on the interval [0, 6]. Assume also that f' is increasing on…

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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: 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: 2. Find the critical points of f(x, y) = x³ + 2y³ – xy and analyze them using the Second Derivative…

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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 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: (a) By using the chain rule and the derivative (1, if x>0 4 (1xl) ={-1, if x<0 %3D find (lx-x) vxE…

A: Use the chain rule to differentiate the above given function and than use the given derivative of…

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

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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: 4. Determine if 1 1 sec if – 1 1 x – 1 is continuous or not at x = 0 and 1. In the case of…

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

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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 critical numbers of the function.…

A: We have given,           h(x) = sin2(x)+cos(x),   0≤x≤2

Q: (b) Show that f(x) = ln(x + 2) has a unique fixed point in [0, 2].

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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, i, Evaluate the first and second derivatives of the function z=2x4+3x3+2x-5 when x = 4. ii, Find…

A: The objective of the question is evaluate area and find derivatives of given functions.

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…

Q: Find Tn cebtered at x=0 fir akk b for the function f(x) = 1/(1+x) at a=0

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.