Consider the following function. f(t) = 4t + 5 Find its average rate of change over the interval [1, 3]. Ay At Compare this rate with the instantaneous rates of change at the endpoints of the interval. f'(1) f'(3) :

Q: 7ェ +8 If f(x) = find: 4x +3 f'(x) = !! f'(4) =

A: The objective is to find f'(x) and f'(4).

Q: Implicit Differentiation. The demand equation for a certain brand of two-way headphones is 3x³-8xy +…

A:

Q: Determine the of : In (xy²) = x y dx

A: Derivative dydx of equation  lnxy2=xy

Q: Given that the graph of f(x) passes through the point (6, 9) and that the slope of its tangent line…

A:

Q: 4. Represent each of the following in the exponential form: (a) 1+i (b) Vz (c) Vi, V-i

A:

Q: dx (x – 2)Vx² – 4x +3 dx sin-1xV1- x2 L. cos(sec xVx2 – 1 -x) dx 2/V3

A:

Q: b) dx xV5x2 – 4 c) dx 2 + (x - 1)2 d) . /2 2 cosx dx 1+ (sin x)²

A:

Q: Question Consider a continuous function f(x). The function has critical points at.x = -2, x = 2, and…

A: topic - application of derivatives

Q: Betermine whether the Mean Value theorem can be applied to f on the closed interval [a, b)]. (Select…

A:

Q: 2² + y° = 1 = 2' - y %3| = z + y? = 1 +E z = I +y ² + y² + z² = 1 = 2° + y? circular cone sphere…

A:

Q: Describe the graph of the equation. r = -9i+ tj + (r² – 1) k O It is a parabola in the x = –9 plane,…

A:

Q: You are driving a car away from home. Your velocity​ (miles per​ hour) t hours after noon is given…

A: Given:       vt=-5t4+40t3-149t2+180t  Distance you drove between 1:00pm and 2:15pm is given by…

Q: * TO 7. Determine a function whose graph has vertical asymptotes at x = ±2 and a horizontal…

A: The objective is to determine the required function.

Q: (1 2. 14 Approximate | * -6) dx using 4 rectangles. It is approximatley : (If necessary, round to…

A:

Q: Use the second derivative to determine the intervals on which the given function is concave up and…

A:

Q: Electric Current. Suppose you have two electronic devices that have different currents when x = 2.…

A:

Q: ピ+5 1 lim t一+0|5t2 +6'2t (?, ?)

A:

Q: Choose the point which shows the correct location for the polar coordinate (-2, – 3). 90° 2 45° I 4…

A: The point is -2,-3π4

Q: Y1=25-82 = 25 – x², Y2 = 0 Y1 = Rotate @ y axis SHELL METHOD B V = 2 · T • (C·a - aº) · dE = G A…

A:

Q: 13. Find the inverse of A= 1 1 Use any method. Show your solution. 0 2 3 55 1J

A:

Q: Cost Function. Suppose the cost to manufacture a product is given by f(x,y) = ey? The domain of…

A:

Q: mutliple choice- I need help asap please!

A: a. limx→-4+f(x)    This limit means what is value of f(x) when we approach -4 from right(right…

Q: Given f''(x) = 9x – 5 and f'(– 3) 5 and f( – 3) = 4. %3D a? - 5æ - 121 Find f'(x) 2 and find f(3)

A:

Q: Use the formula k(t) ||r'(t) × r"(t)|| to find k(t). ||r(t)| r(t) = 11 cos(t)i+ 11 sin(t)j + 6tk

A:

Q: Let ā = (– 1, 4) and b = (4, 5). Find the projection of b onto ä. proją b > Next Question

A: answer is in next step

Q: Use the shell method to set up and evaluate the integral that gives the volume of the solid…

A:

Q: Suppose that in a certain country the life expectancy at birth of a female is changing at the rate…

A: We have to find an expression and life expectancy (in years) at birth of a female born in 2000.

Q: Find f (x) if f'(x) = and f(1) = 25. O f(x)= 16x + 25 O f(x) = 16x +1 O f(x) = 16xl +9 O f(x) = 16x…

A:

Q: d Calculate r1(t)·r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly and…

A:

Q: Integrals. Given that 0. -1 f(x) dx = -2, | f(x) dx = -1 and -5 f(x) dx = 8 -5 what is 2f(x) dx? O7…

A:

Q: Integration by Substitution. The rate of growth of Grass carp, one of the most common type of fish,…

A:

Q: Given the power series Σ 2 n A, x" n = 1 Use the technique that we covered in this lesson to force…

A:

Q: Let u = (-3, 2), v (0,-1) and A = %D %3D %3D NOTE: Give ezact answers. (a) Find ||u|| relative to…

A:

Q: The number of bacteria P (h) in a certain population increases according to the following function,…

A:

Q: Flight of a Rocket. Suppose the altitude (in metres) of a rocket t seconds into flight is given by…

A:

Q: 2. In addition to obtaining the domain and range, provide a sketch of the graph of the following…

A:

Q: Select the answer option that corresponds with polar coordinates (4, –120\degree). 兀 90° 2 WIN 135°…

A:

Q: Let å = (2,0, – 3) and b = (0, 1, 5). Find b x a.

A: Given query is to find indicated vector.

Q: Given the power series 00 2 A x(n + 3) n = 0 1. Force the Exponent "n + 3" to be "R" like we did in…

A:

Q: For the function f(x) = 2x – 2x, evaluate and simplify. %3D f(x + h) - f(x) %3D

A:

Q: n(3n – 1) - 1+4+7+...+ (3n – 2) =

A:

Q: Evaluate the integral using appropriate substitution. an NOTE: Enter the exact answer. sin (80) d0…

A: The given integration,θ    ∫sin38θ dθ

Q: Determine whether the following statement is true or false. If f'(c) = 0, then f has a relative…

A: To determine true or false.

Q: 6. (Section 4.3) Find the area under each curve over the indicated interval. (a)y = 6- x2, (-2, 1]…

A:

Q: 1) Find the second derivative of y = csc 2 e cot 2e %3D

A:

Q: Integration by Substitution. The rate of growth of Grass carp, one of the most common type of fish,…

A: The given data is: ∫025x+10x2+4x+4dx

Q: 30 If g(y) - (v- 11y + 18) lly + 18)*, find g'(y) = 30(v - 1ly+18) ) 29 (2y – 11)

A:

Q: For the function f(r) = - 2x – 5x, f(r + h)- f(r) evaluate and simplify: h Find the value of the…

A:

Q: Find the gradient field of the function, g(x,y,z) = e 3z - In (x +2y).

A:

Q: Use implicit differentiation to find the specified derivative at the given point. dy 7. Find at the…

A: Given that,   6x-7y+5x2y2=0 at the point -1,1