b Use calculus to prove that the relative minimum or maximum for any function f, as shown below, occurs at x = - 2a f(x) = ax² +bx+c, a‡0

Q: Find the absolute minimum and absolute maximum values of f on the given interval. (Enter your…

A: we need to find out the absolute minimum and absolute maximum of the given function in the given…

Q: d-L question

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Consider the indefinite integral The integrand decomposes into the form ax + b + where a = b = C =…

A:

Q: 5n (c) Σ(-1)"-1 3n-1 n=1

A: Consider the series

Q: The function f(x) is graphed below. What is true about the graph on the interval from point d to…

A: Consider the graph

Q: Using indirect or direct proof methods, prove for every positive integer n, n2 + 6n + 5 is not…

A:

Q: •π/2 1 [™ ² + xy cos(x²y) dx dy

A: Evaluate the double integral.

Q: Use graph below to calculate the following: (a) f(f(2)) = (b) g(g(2)) = (c) f(g(4)) = (d) g(f(4)) =…

A: A graph of the functions  and  are given.The aim is to find the composite function values  and .

Q: Let f(x) = 2logs(r) ƒ'(x) = f'(7) =

A:

Q: Given that g(x) + 7x sin(g(x)) = 48x² − 26x — 35 and g(— §) = 0, find g’(− §). g ( − § ) = =

A:

Q: Write all the calculations needed to find the eigenvalues corresponding eigenvectors V+ of the…

A:

Q: Approximate √4.2 using tangent line approximation First note that √4.2≈ √4. Let f(x)=√x. Then, f'(x)…

A: we need to find the  using linear approximation.

Q: Consider the piecewise defined function Find the values of a and b that make the following function…

A:

Q: Find the derivative of the function f(x) = O 4x³ - 2e²x -sin 3x x4-2x sec Br O-4x³e-2x cos 3x -…

A:

Q: The altitude of a triangle is increasing at a rate of 2.5 centimeters/minute while the area of the…

A: Given -The altitude of a triangle is increasing at a rate of 2.5 centimeters/minute Area of the…

Q: (c) This graph is a rose curve (d) π/2 π/2 2 3 4 5 6 7 8 I with equation 0

A:

Q: Simplify the expression completely. /−1 - 4√−125 + √64 +2√9

A:

Q: (a) Use the table of values for f(x) and the graph given for g(x) to calculate each of the…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: A street light is at the top of a 19 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A:

Q: Find the absolute maximum and minimum points of f(x) = In (5x2 - 5x+3) in the interval x = [0,2].…

A: To find the absolute max and absolute min, we have to check the values of f(x) at the endpoints and…

Q: (a) Compute the integral (b) Compute the integral sec Ode by observing sec 0 = sec (tan+sec 0) tan 0…

A: The given integrals(a) (b)

Q: Describe the given region in polar coordinates, such that 0≤r and 0≤0 ≤ 2. C 1 2√3 ✔ The lower…

A:

Q: Suppose f(x)=7(2.5)^x and g(x)=55(1.4)^x. Solve f(x)=g(x) for x.

A: Suppose .To solve  for .

Q: f(æ)=-5x*+1 x y -2 -1 0 1 2

A: We need to find that the function is even or odd.If f(-x) = f(x),  then the function is even.If…

Q: Find the inflection points for the function f (x) = 8x - sinx, ≤ x ≤ 7 < O (π, 8π), (2π, 16T + 2) ○…

A: The given function is  ,

Q: Question 3 Find all critical values for f(x) = 5x³ – 9x² - 6x - 71. The critical values occur at x =…

A: The critical points of a function f(x) are the values of x for which f'(x)=0.

Q: Determine whether the series is convergent or divergent. 3 1 3 + + 16 32 64 1 3 2 + + + 4 8 O…

A:

Q: If 87 + 2 f(x) + 3x² (ƒ(x))³ = 0 and ƒ(1) = −3, find ƒ'(1).

A: 87+2f(x)+3x2(f(x))3=0,f(1)=−3

Q: Experiment 3:  3A.  Slide the large circle on the parabola so the small circle on the x-axis is at x…

A: The objective of the question is to understand the relationship between a function and its…

Q: A conical water tank is 6m high and has a radius across the top of 3 m. The tank is filling with…

A:

Q: In preparation for the next problem, find the derivative of the EXPONENTIAL function. (This does NOT…

A:

Q: When does the function ()-x(x-1)" have a local minimum? a) (0, 0) O b) (1, 1) c) (-1,0) d) (1, 0)

A:

Q: y rides a train along a straight north-south track. His position at timet in hour is s(t) = (–t¹ –…

A: We have to find the average velocity, instantaneous velocity.

Q: Suppose that the distances and y are changing with respect to time and satisfy the equation x² + y²…

A:

Q: Simplify the expression to a + bi form: (8 + 3i)(4 + 4i)

A:

Q: Oil has spilled in the ocean. The volume of oil in a spill in the shape of a cylinder of height 6…

A:

Q: Find the absolute maximum and minimum y-values of f(x) = x - 4 In(x) on the interval decimal…

A: Consider the function

Q: 3. Determine whether the series converges or diverges. If it converges, find its s 3n+1 ∞ ∞ (a) (b)…

A: Find whether  series  converged or diverges

Q: Question 4 Let y = sin(4x). If Ax = 0.2 at x = 0, use linear approximation to estimate Ag Ay~= Find…

A:

Q: what number exceeds its square by the maximum amount?

A:

Q: Find the derivative of f (x) = ln O f'(x) © f'(x) O f'(x) O f'(x) = = = = | 8 + sin x f (x) = ln (…

A:

Q: Consider an oblique triangle ABC with sides a = 6 cm, b = 9 cm, and an angle C = 320. Find the angle…

A:

Q: Suppose a company's total cost for a product is given by C(x)=30000-60x+0.3x^2 and the total revenue…

A:

Q: The total cost function for a product is C(x) = 875 In(x + 10) + 1600 where x is the number of units…

A: We need to find the cost of 200 units of product in (a) and find the no. of products which will have…

Q: Find all points of intersection of the given curves. (Assume 0 ≤ ≤ 2m and r20. Order your answers…

A: To find all the points of intersection between the two polar curves r = 2 and r = 4sin(2θ), we need…

Q: Find the interval in which the function is X decreasing f(x) = 2²+4 ○ (2, ∞) O (-2,2) ○ (-∞0,00) O…

A:

Q: b) A rectangular box with a square base is designed to have a volume of 8ft³. The material used to…

A: The rectangular box is given by:

Q: Simplify the expression to a + bi form: (1 − 4i)(−11+ 3i)

A: Simplify  the given expression

Q: Simplify the expression completely. 49 +4√−9+ √512

A:

Q: Find an equation for the conic that satisfies the given conditions. parabola, vertex (6,-3),…

A: Given the vertex of the parabola (6,-3) , horizontal axis, and passing through the point (-44,2) we…