Find the intervals on which​ f(x) is​ increasing, the intervals on which​ f(x) is​ decreasing, and the local extrema.   ​f(x)=4x2−40x+1

Q: Find the area of one petal of the rose curve r = 3 cos 30.

A: Let's find.

Q: Find a formula for the slope m of the graph of f at the point (x, f(x)). Then use it to find the…

A:

Q: Use the formula k(t) ||F(t) × r"(t)|| to find k(t). ||r(t)||° r(t) = 11 cos(t)i+11 sin(t)j+6tk K(t)…

A:

Q: (b) f(x, y) = 3.03 + 3y2 – 4 ln y, a = 0, y = 1, dr = 0.01, dy = -0.01. since fa (x, y) = 3.3x-1+ 0…

A:

Q: Problem 9 Solve the following Cauchy-Euler equation: ²y" +3ry +17y = 0

A:

Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

A: Differentiate R and C with respect to time .

Q: Consider the function f(x) = 4T + 3 on the interval (2, 5]. Find the average or mean slope of the…

A: use slope formula for finding the slope of f(x).and value of c

Q: Bones from the skeleton of a fish have lost 30 percent of their carbon-14. Note that for carbon-14,…

A: Formula  Given  k = 0.000124 It lost 30 percent of carbon  The left is 70 percent

Q: 1. Determine the absolute extrema of f(z) = (sin a – 1) cos z on -. 2 if they exist, and identify…

A:

Q: C. VARIATION OF PARAMETERS 1. (D² + 1)y = secx tanx 2. (D2 – 3D + 2)y = 1 1+e-x

A:

Q: Let a > 0 and let R be the region under the graph of f(x) =  √(9 - ax) and in the first quadrant.…

A: Points of intersection:y=x =9-axx=9-axx+ax =9x=91+aPoint (91+a, 31+a)

Q: Determine Y for y= 5x²(1 + x²).

A:

Q: The position of a particle moving in a straight line is given by s() =- 8² + 28r, where s(t)…

A: Solution )  s(t) = t3/3 - 8t2 + 28 t  Differentiate with respect to t   v (t) = s'(t)  = 3t2/3 - 8×2…

Q: Use a double integral in polar coordinates to find the volume V of the solid bounded by the graphs…

A:

Q: Solve the initial value problem. + x, x > 0; y(1) = 5 y = y = - 2x- +5 2x y = 2x2 2

A:

Q: 1. Let f be a function satisfying the following properties: continuous on R\{1} • f(0) = 0 and f(3)…

A:

Q: a) Find the fifth term of the sequence 16 31 46 61 9' 15' 21' 27 b) Find the general term of the…

A:

Q: y a+h Figure 1.3.2: Plot of y = f(x) for Preview Activity 1.3.1. b. Construct a right triangle whose…

A:

Q: п+1 Given that 0.47199 determine the value of ) n +1 n3 n=3 n3 n=5

A: Given: ∑n=3∞ n+1n3 =0.47199 To evaluate: ∑n=5∞ n+1n3

Q: Determine whether the following series converges or diverges. Σ 5n2 +5 n=1

A: We can solve the given problem as follows:

Q: Consider the following lines defined by I,: x – 3 = y – 5 = z – 6 and I2(t) = . c) Determine if the…

A:

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A: Solution is given below:

Q: B. NONHOMOGENEOUS EQUATIONS: UNDETERMINED COEFFICIENTS 2. (D2 + D – 2)y = 2x – 40cos2x 3. (D² + 1)y…

A:

Q: (a) Find an equation of the tangent line to the curve y 14x sin(x) at the point (x/2, 7n). y = (b)…

A: a) y=14xsin(x)Differentiatey'=14sin(x)+14xcosxSubstitute x=π2y'=14sinπ2+14π2cosπ2y'=14+0y'=14Slope…

Q: Evaluate the definite integral. NOTE: Enter the exact answer. 11

A:

Q: Find all points on the graph of ƒ(x) = 2 sin x + sin?x where the tangent line is horizontal

A:

Q: p(x, y, z) 4 – x² – y²

A:

Q: (c) Determine whether the following function continuous at point (1, 1). Justify your answer. (x²-xy…

A: To determine whether the following function is continuous at the point 1, 1.fx, y=x2-xyx-y  if x,…

Q: Step Pattern From Vertex Equation Vertex Direction Describe of Transformations Opening y = -2(x +…

A: 1. y=-2x+72+8vertex formy=a(x-h)2+k  vertex = ( h , k ) = ( -7 , 8 ) x y -6 6 -5 0 -4 -10…

Q: From Rogawski ET 2e section 10.2, exercise 36. Use the formula for the sum of a geometric series to…

A:

Q: Let f(x) = r³ – 3r² + 4. Using the Mean Value Theorem, determine the value of c € (0, 3) such that…

A: f(x)=x3-3x2+4 Here f(x) is polynomial in 'x', (i) f(x) is continuous on [0,3] (ii) f(x) is…

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) V…

A:

Q: Determine whether the following function continuous at point (1, 1). Justify your answer. (x²-xy if…

A: Here we have to determine whether the given function is continuous or not.

Q: Find the equation of the tangent line to y = 7et at x = 3. (Use symbolic notation and fractions…

A:

Q: 1. sin²(esin*r) + cos-(2t³ – 5)

A:

Q: y= V x

A: Here is the solution

Q: From Rogawski ET 2e section 10.2, exercise 11. Calculate S3, S4, and S5 and then find the sum for…

A: Sum of First n terms: = (1/10 - 1/11) + (1/11 - 1/12) + (1/12 - 1/13) + (1/13 - 1/14) + (1/14 -…

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

A:

Q: The term a,6 of the sequence {an} given by (2 3 4 5'7'9' 11

A: Follow the procedure given below.

Q: Question Solve the following equation exactly where 0 < 0 < 2ñ. 3(csc? 0 + 5) = 21 Select all…

A:

Q: 1 у 3 2 y (х + 2)

A: y = (x+2)-1/2 dy/dx = (-1/2)(x+2)(-1/2 - 1) dy/dx = (-1/2)(x+2)(-3/2) dy/dx = -1/2(x+2)3/2

Q: evaruate 6 (i-1) 13. +=3

A: Open the summation for the given value  of i

Q: Find the curl of the vector field F = (4x sin(y), 7y cos(x)). curl F - Dretieur

A:

Q: Test the series for convergence or divergence. E sin? n n+ 3n

A: Given

Q: Determine if the sequence is increasing, decreasing, not monotonic, bounded below, bounded above…

A:

Q: Solve the area of the surface of the revolution generated by revolving the arc of the curve, x= y³…

A: A detailed solution is given below.

Q: Sketch the region R of integration and switch the order of integration. f(x, y) dy dx y Show ,…

A:

Q: Solve the following system of differential equations. dx —х — у, || dt dy Зх — у dt

A:

Q: As shown in the figure below, Ann is standing 36 feet from the base of a leaning tree. The length of…

A:

Q: 4. For each of the following, state whether the equation is ordinary or partial, linear or…

A: here derivative of first order so order 1 here power of x is 2 so non-linear and ordinary equation…