3. Iff has a local maximum at x – 1, then what can you say about f'(1)? What if you also know that f is differentiable at x = 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: The oxygen supply, S, in the blood depends on the hematocrit, H, the percentage of red blood cells…

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Q: Find constants a and b in the function f(x) = axe“ such that fE) = 1 and the function has a local…

A: The given function is fx=axebx. It is given that f15=1. So, f15=a·15·eb·151=aeb55aeb5=5

Q: Find the minimum and maximum values of the function on the given interval by comparing values at the…

A: The given function is y=cos θ+sin θ

Q: Find the critical numbers of the function

A: We find the first derivative

Q: Please show your answer to at least 4 decimal places. Suppose that f(x, y) = x² – xy + y² – 5x + 5y…

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Q: At waht x does f(x) have a local(relative) maximum?

A: A function f(x) is defined for x values there are local maxima and local minima in the given curve.

Q: Find the minimum and maximum value of the function on the given interval by comparing values at the…

A: To find the minimum and the maximum, first, calculate the first derivative of the function, y=5…

Q: 3 (a) Determine exact locations of critical numbers of the function f(x) COs x + cos 2x

A: for finding critical point take f'(x)=0

Q: A differentiable function f has only one critical number at x = 5. What can we say about this point…

A: If first derivative is negative on left side of critical point and positive on right side, then it…

Q: The oxygen supply, S, in the blood depends on the hematocrit, H, the percentage of red blood cells…

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Q: The function f has a continuous second derivative, and it satisfes f(2) = 5, f'(2) = 0 and f"(2) =…

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Q: 2. Find the interval [a, b] for which the value of the integral (2 + x − x²) dx is a maximum.

A: ∫ab(2 + x -x2 )dx here for get maximum value we have to differentiate the function  so here first…

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 function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0. ƒ(x) has a root in [0,1]. If we…

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Q: 2. Suppose that f(x) is a function continuous for every value of x whose first derivative is f'(x) =…

A: Given: f(x) is a function continuous for every value of x whose first derivative is f'x=21-x1+x2 and…

Q: Find the points at which y=f(x)=4x−ln(2x)y=f(x)=4x−ln⁡(2x) has a global maximum, a global minimum,…

A: Given function

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: 1. Suppose that f(x) = -ar/2 + bæ/2. Reparameterize this function in terms of the location of the…

A: given fx=-ax32+bx12 differentiate the function with respect to x f'x=-32ax32-1+12bx12-1…

Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate In(1.18). L(x) =…

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Q: Find the critical points of the following function.   f(x) = 1/x - ln(x)

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Q: 6. Locate the absolute extrema of the function H(x) = - x* Inx on 1 3 2' 2 Give exact solutions.

A: We have to find out absolute extrema

Q: What is most nearly the magnitude of the maximum error in the linear interpolation of the polynomial…

A: Given function is yx=cosx

Q: Find the critical points and the local and absolute extrema of the following function on the given…

A: To find the critical points, local and the absolute extrema of the following function,…

Q: Use the Mean Value Theorem to show that f(r) = 2x sinh(x – 1) + 2" – x %3D has a critical number…

A: Given: We can see that the function is continuous in [0, 1] and differentiable in (0, 1). So, the…

Q: 3. The function f(x) = x^4 − 4x^3 + 8x has a critical point at x = 1.(a)  Find f"(x).   (b) Then use…

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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: 1 5. By using the cubic approximation of f(x) = --1 around a = 0 in question 4, estimate the error…

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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: 5. Suppose f is twice differentiable at xo. If f'(xo) = 0 and f"(x,) > 0, then (a) f has relative…

A: As we know if f(x) is continuous in the domain then and there is a point x= a exist such that

Q: 13.Find a sinusoidal function with a maximum value of 9 that occurs at x=4 , and a minimum value of…

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Q: Find the absolute maximum and absolute minimum values of the function f(x) = 2x – 15 In(7x) on the…

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Q: Find the exact location of all the relative and absolute extrema of the given function. f(x) = x -…

A: Given : f(x)=x-lnxdomain: (0,∞) To find out absolute minimum or maximum , we take derivative with…

Q: find the minimum and maximum value of the function on. the given interval by comparing values at the…

A: Given function is Firstly, we find critical points of y=f(x)  Also, given function is defined for…

Q: Approximate the critical points of g(x) = x cos−1 x and estimate the maximum value of g.

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Q: If the function f(x) is defined on the 2 intervallo, TT) and f'(x) = -cos X (sinx) than f(x) has…

A: Given that fx is a function defined on an interval 0,π whose derivative f'x=-cosx1+sinx2 To find the…

Q: 14. Give the linear near-minimax approximation for f (x) = sin a on [–1, 1].

A: To determine linear near-minimax approximation for fx=sinx on -1,1 Let the approximation be px=a+bx…

Q: Given the function y"=-6X(x²-ax+4) (x+a)³ (x -1)³ 3. with (X+2)(x-) - analysiS Enclude all maximums…

A: given that y=-x3x+2x-2find the maxima and minima for the given function

Q: Discuss the extreme-value behavior of the function ƒ(x) = x sin (1/x), x ≠ 0. How many critical…

A: Given fx=xsin1x,x≠0

Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: Given function:                         y=ex-e-x The domain of a function is the set of input values…

Q: On the number line, mark the critical value(s) of f(x) and the sign of the first derivative between…

A: From the given graph of f'(x) to answer the given questions.

Q: 7 If the change of variables u = x-1 is used to evaluate the definite integral f(x) dx, what are the…

A: This question can be solved using the concept of change of limits in definite integrals.

Q: Consider the Cobb-Douglas production function f(x, y) = 100x1/3y2/3 where x is the number of units…

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Q: 12. If z = 2xy – 3x²y and x is increasing at 2 cm/s, determine at what rate y must be changing in…

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Q: . Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0. f (x) has a root in [0]. If we…

A: Newton-Raphson iteration scheme is given by  xn+1=xn-f(xn)f'(xn) We use this formula to estimate…

Q: ind the x-coordinates of all critical points of the given function. Determine whether each critical…

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Q: 39. Use Leibniz's Rule to find the value of x that maximizes the value of the integral px+3 1(5 – t)…

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Q: Find the critical points c for the function f and apply the Second Derivative Test (if possible) to…

A: Given:The given function is f(x)=20x11ln5x    (x&gt;0)To find:the critical point c for the…

Q: 2. Consider the function h(x)=8+(x+3)*x"3 . a. Find all critical numbers for the function h(x).

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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