3. Analyze the function f(x)=x°+2x* +8x' +16x² –9x–18. Follow the steps below; show a work for full credit. a. Describe the end behavior (prediction for y as x → to) of the graph. (Explain how you know.)

Q: m Find the equation of the tang ent to the curve ym =1 at the point (x1.y1). m

A: Topic:- application of derivatives

Q: Q5: Does any tangent to the curve y vx cross the x-axis at x--1 If so, find an equation for the line…

A: It is required to find if any tangent to the curve y=x cross the x-axis at x=-1. First find the…

Q: C. If h(x) = [f(x)]² + g(x),what is the equation of the line tangent to the graph of h at x = -2?…

A: First we will find derivative of h(x) at x=(-2) that gives the slope of the required tangent.

Q: Determine the missing coordinates of the points on the graph of the function

A:

Q: 1) Find the legth of the curve; y = e from x =1 to x = 2.

A:

Q: 2. Let f(æ) = 2e* – 3x² /a, whose graph is given to the right. Sketch in the tangent lines to f(x)…

A: Graphed the tangents using a graphing calculator.

Q: 6. Find the point on the curve y = yx that is closest to the point (3, 0)

A: let P is the closest point then say (x,y) then find the distance from the point (3,0)  then minimize…

Q: 4 - Find the direction A in which the function f(x, y) = x cos y + y sin x decreases most rapidly at…

A: We have to find the direction A in which the given function decreases most rapidly.

Q: h (x) = [ƒ (x)P + g (x), what is the equation of the line tangent to the graph of h at x=-1?

A: Given,           hx=fx2+gx

Q: 1. Find for y defined implicitly by the equation dx

A:

Q: 19. Find the equation for the line tangent to the given curve y f(x) at the point P. (a) f(x) =…

A: Given, f(x)= 2x²+5x-10 P=(x,y)=(1,-3)

Q: Use differentials and the graph of f to approximate (a) f (1.9) and (b) f (2.04). To print an…

A: To calculate the approximate value of a) f(1.9) and b) f(2.04)

Q: Find the length of the graph of ; a. f(x)=⅓x2 -⅔ between x=2 and x=3.  b. x=cost, y=sint from t=0…

A: See the detailed solution below.

Q: (ii) Find the length of the curve y = E* from x = 0 to x = 2. %3D

A:

Q: Q6. Find the equation of the tangent line to the graph f(x)=2xsinx at x=n

A:

Q: The graph of the function y = 3 sinh 4x has a relative maximum at a point O (0.0) O (0, 3) O (3.0)…

A:

Q: Q2/Find the length of the curve T = sino + cose between -s0s

A:

Q: Consider the following. a) Verify that the given point (7,7) lies on the curve. x3 + y3 = 14xy b)…

A:

Q: tiny, no bug lands on a piece of graph paper and walks along a path so that t minutes after it…

A: Increasing function

Q: d y is a function of tin

A:

Q: Q4: Find an equation for the line tangent to the curve 2y cos x = 4x sin y , at the point where x =…

A:

Q: Find the value of 'a' for which the tangent to the curve f(x) = (a + 2) x³ − 3ax² +9ax - 1 never…

A:

Q: Find dydx, where y is defined as a function of x implicitly by the equation below. y3+2x2y5=1

A:

Q: Find the equation of the line tangent to fƒ(æ) = e² (x² + 3x) at the point (–2, –2e¯²). O y = -3e-2…

A:

Q: 1. Find the equation of a curve that passes through the origin and satisfies (1 + x²)y' + 2xy = 4x²

A: Given differential equation is  1+x2dydx+2xy=4x2 Simplify the given differential equation we get…

Q: 19. For what values of the constants a and b is (1, 3) a point of inflection of the curve y = ax³ +…

A: Consider the value of y and solve:

Q: Q5: Does any tangent to the curve y = vx cross the x-axis at x=-1 If so, find an equation for the…

A: To find: The equation of tangent to the curve y=x if possible. Given: The equation of the curve y=x.…

Q: 1. Find the equation of a curve that passes through the origin and satisfies (1+x²)y' + 2xy 4x2

A: To find the equation of the curve

Q: I grad(f)•dr where C is graph of y = x² + 3x from (0,0) to (2, 14) and f (x,y) = ev/lx*•1}

A: The function is fx, y=eyx+1. Find: ∫Cgradf·dr…

Q: 9. Find the direction of zero change for the following function at given point (Баллов: 2) xy + y,…

A:

Q: Find an equation for the line tangent to the graph of f(x) = 7re %3D at the point (a, f(a)) for a =…

A:

Q: Find the Giniindex for the lorenz curve L (X)= 0.3X + O=7X 11

A: Given the Lorenz curve Lx=0.3x2+0.7x. Find the Gini index of the Lorenz curve.

Q: 1) Find the Linearization x of the function -V1+2x when x is near 0 Find the equation of the tangent…

A: As per Bartleby guideline if more than one question is asked only first question to be answered…

Q: Solve the following initial value problem for y as a function of x. dy X- 3Dx? -9, х23, у(3)%3D0

A: By using integration formulas

Q: (a) Find the slope of the line tangent to the curve y = sin x at the point where x = T/3. (b) Show…

A: (a) we have to  find the slope of the tangent line to the curve y=sin5x at the point where x=π3. as…

Q: Sketch the graph of y = -3 sin(x) on the axes below. 4 3 2 -7/2 7/2 37/2 27 -1 -2 -3 -4

A:

Q: 1. Any function y = f(x) can be expressed as x = f(y) in standard mathematical methods for solving…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Given the equation y In (x+y +6) 36, evaluate Assume that the equation implicitly defines y as a…

A: The equation is given by y lnx2+y4+6 = 6…

Q: 10. Find the points of inflection of the curve y f(x)=x³ -x.

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Q5: Find an equation of the tangent line to the graph of f at (1, 32): y = x (x + 1)5

A: The slope of tangent at any point on the curve is given by the value of derivative of that function…

Q: that is tompent ☺ Find the equation to the the Cime curve of fG)= (4-3)9 at x =l 4 (Tes f(x) =…

A: according to our guidelines we can answer only three subparts, or question and rest can be reposted.…

Q: Find the point on the curve f (x) = Vx that is closest to the point (2,0). Put your answer in the…

A: Use distance formula and differentiate and put zero

Q: h(x) * |4x + 1 %3D a) Find the equation of the line tangent to the graph of fx) at x = 2.

A: 8). Given function is hx=4x+1. To find: (a). The equation of the line tangent to the graph of fx at…

Q: Choose the correct graph of y = sin x, -"sxS T: 1 -37 21 -1 -2

A: The given function is: y=sin x ;                 -3π2≤x≤π

Q: Does the graph of S0, x< 0 U(x) = 1, x2 0 have a vertical tangent line at the point (0, 1)? your…

A:

Q: How can I get the result? Which is the result?

A: The function is given by,

Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

A:

Q: Sketch the graph of y = t + sin t for 0 ≤ t ≤ 2π.

A: The given function is y=t+sin t    for  0≤t≤2π. Sketch the graph of the above function as shown…