Find all critical numbers c of f(t) = 3t²/³ +t5/³.

Q: Find f'(1) if f(x)= x + 1 √x + 1 A

A: we need to find the derivative of function at point x=1.

Q: ·b f(b) − ƒ(a) = f'(a)(b − a) – ſå ƒ''(x)(x − b)dx a

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Q: b) Consider the triangle formed by the side of the house, ladder, and the ground. Find the rate at…

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Q: Help determine the difference quotient and for f(x)=x^2+4

A: Given,. Difference quotient=

Q: 1) State the order of the given ordinary differential equation. Determine whether the equation is…

A: Order is the highest power of the derivative Degree is the power on the highest power of the…

Q: Q/ solve equations 1- y' = ky 2-x(1+y²) dx =y(1+x²) d;

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Q: 4. Use Calculus to graph g(x)=x² + 4x³. Make sure that your graph shows all intercepts, extrema, and…

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = 2t²1 - 4tj + (a) r(t) (b) r"(t) (c)…

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Q: Let L denote the left-endpoint sum using n subintervals. Compute the indicated left sum for the…

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Q: Solve the following non-homogeneous differential equations: 1) x"(t) + x(t) = 2 cost

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Q: Find the derivative of the function at Po in the direction of A f(x,y.z)= - 3e cos (yz). Po(0,0,0).…

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Q: Consider the following differential equation to be solved by the method of undetermined…

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Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 4 + x² -…

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Q: The indicated function y₁(x) is a solution of the associated homogeneous equation. Use the method of…

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: The function is given byTo determine: The absolute maximum and minimum values of the function.The…

Q: A mutual fund is currently valued at $70 per share and its value per share is increasing at a rate…

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Q: 0 1 3 2 X f(x) f'(x) -2 -1 2 N 2 133 When x = 0 then D 1 255 324 X 0 3 g(x) 1 2 g'(x) 2 3 -2 0 g(x)…

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Q: If lim f(x) = 4 →2 then compute the exact value of x + f(x) lim x→2 Enter your answer as a decimal…

A: The Root Law:The Sum Law:

Q: = O Trigonometric Identities and Equations Proving an identity using fundamental trigonometric…

A: 1+tan2x

Q: Use the Table of Integrals in the back of your textbook to evaluate the integral: sec² (9t) tan²…

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Q: Use the alternative form of the derivative to find the derivative of the function f(x) = x³ + 8x, X…

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Q: Find aw/as and aw/ât using the appropriate Chain Rule. Values Function w = y³ - 2x²y x = es, y =et S…

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Q: (b) Suppose that f(x) = 2x^2 − x^4 . Find the intervals on which f is increasing and those on which…

A: Question no. (b):Suppose that To find the intervals on which is increasing and those on which it is…

Q: Find aw/as and aw/ât using the appropriate Chain Rule. Function Values w = y³ - 2x²y x = es, y = et…

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Q: For which value of t does the line given by the parametric equations x = t - 1, y = 1+ 2t, z = 3-t…

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Q: Evaluate the following integral, f (x - 5y) dx - 8y² dy where C' is given by x = y² + 6 from (7, 1)…

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Q: Consider the function f(x) = -2x³ + 36x² - 192x + 1.

A: f(x)=−2x3+36x2−192x+1

Q: Let 16x-5 1x² +5 Enter the exact value of the one-sided limit lim f(x) 3-2 f(x) = if x ≤ 2 if x > 2

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Q: Consider g(z) = -10z + 15z² - 9 Determine the intervals on which g is concave down. g is concave…

A: The given function .The aim is to find the concavity intervals and the inflection point.

Q: Estimate f (5.06) for f as in the figure. y=f(x)/ ƒ (5.06) ≈ (4,2) (10,4) Tangent line X (Give your…

A: The figure is given as,Estimate

Q: The median home value in Texas and Missouri (adjusted for inflation) are shown below. Year Texas…

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Q: (4) y' + (x + 1)y = ex²y3

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Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

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Q: 17 [²²; 1 The integral dx diverges. x (In x )1.5 If the integral converges, enter the value below.…

A: Substitute

Q: Find the total differential. 8x + y 3z - 2y dw = W X

A: If W = f(x,y,z) then the total differential of W is given by   +

Q: differentiate y(theta) = e^cot theta

A: given function

Q: .SS. Write an iterated integral for dA over the region R described to the right R using a. vertical…

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Q: Consider the following parametric curve. x = sin(t), y = cos²(t); (√2-1) Find an equation of the…

A: The slope of the tangent line to the parametric curve. If x = f(t), y = g(t)   a<= t <= b at…

Q: Find the inverse matrix where A = 1 -1 2 -3 -3 1 2 -3 -3

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Q: SYSTEM: x + y + z = 6 2x - y + z = 3 3x z = 0 -

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Q: ketch the region of integration, reverse the order of integration, and evaluate the integral. 10 10…

A: First sketch the curve by use of the limit of integration.

Q: Find the measures of the sides and angles. Round angle measures to the nearest tenth of a degree.…

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Q: 6. Logarithmic differentiation Use logarithmic differentiation to evaluate f'(x). f(x)=(1+x²)in x

A: The given function .The aim is to find the derivative of the function using the logarthim…

Q: Sales The profit for a product is increasing at a rate of $5600 per week. The demand and cost…

A: The profit for a product is increasing at a rate of  per week.The demand and cost functions for the…

Q: A student solves an optimization problem as in Model 1, except that in the problem Mini and Max are…

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Q: Solve the equation for x in terms of the other letters. (Enter your answers as a comma-separated…

A: Given data

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

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Q: Find dy/dx and d'y/dx, and find the slope and concavity (if possible) at the given value of the…

A: The given parametric equations

Q: Use the graph of the function f shown to the right to estimate the indicated function values and…

A: Find the value of the limit

Q: Consider the following. x = e-5t, y = e5t (a) Eliminate the parameter to find a Cartesian equation…

A: Consider the following.To eliminate the parameter to find a Cartesian equation of the curve.