41. Aroller coaster has the shape of the graph in Figure 19. Show that when the roller coaster passes the point (x, f(x)), the vertical velocity of the roller coaster is equal to f'(x) times its horizontal velocity. (x, (1) FIGURE 19 Graph of f as a roller coaster track.

Q: 5. Show that the equation of the tangent to the curve y = Inx + kx at x = 1 always passes through…

A:

Q: 3. Find an equation of the tangent line to the graph of y = log,x at the point ( 32,5).

A: We need to find the equation of the tangent line to the graph of y=log2x at the point (32,5) . Using…

Q: 1. FIND THE SLOPE OF THE TANGENT LINE TO THE GRAPH OF THE FUNCTION f(x) = 5 – x² AT (3,–4).

A: f(x)=5-x2 To find the slope of tangent, we can use two alternatives (1) Direct derivative (2)…

Q: 2. Find the equation of the tangent line to the graph of y = 3cos 4x at x = 3

A: The equation of tangent line can be found by using the formula,y-y1=mx-x1Where, m=dydxx1

Q: 5) Determine the equation of the tangent to the curve y = √3x² - 2x at x=1.

A:

Q: 7. If the tangent line to y = f(x) at (-1,3) passes through the point (2,1), find fl-1) and f'(-1).

A:

Q: Section 2.4 Chain Rule Please show & explain all work, thank you.

A: Multiply both sides by x^2.

Q: what is the slope of the tangent line to the graph of the equation ey = [cosh x] tan−1 (2^x) at x =…

A:

Q: 5. Find the equation of the tangent line to the curve of the function Y= 2x-x +2 at the point (1,3).

A: Given,  y = 2x3-x2+2   and the point 1, 3 We have to find the equation of the tangent line at the…

Q: Find the equation of the line tangent to the graph of f(x) = – = -3 cos (x) at x = 3 m(x – xo). You…

A: given: the function f(x)=-3cos(x) the point is x=-π3

Q: 7. Find the points on the curve y=-x where the tangent line is parallel to the line y= 3x

A: The points on the curve y=x33-x where the tangent line is parallel to the line y=3x

Q: 3) Find an equation for the tangent line to the graph at the specified value of x. y=x²V5-x² ,x=1

A:

Q: 4. Find the slope of the tangent to y = sin² (2x) at x = 12

A:

Q: 4. Find the equation of the tangent line to the curve y = 5x– 6/x at the point (1, –1).

A:

Q: 2 Find the equation of the tangent line to the curve y =xNx +5 at the point (2,6)

A:

Q: Find an equation of the tangent line to the graph at the given point .

A: Given: fx=4xx2+6 We need to find the equation of the tangent line to the graph f(x) at 2,45

Q: 2. Determine the equation of the line perpendicular to the tangent line to the function f(x) = e' at…

A: We will find the equation of the line.

Q: 5. Write the equation of the tangent line to the curve of y = e³x + cos(-x) at the point (0,2).

A:

Q: 4. Find the equation of the tangent line to the function y= In(x* -2) when x=3.

A:

Q: 9. Find all the x-values on the curve where the tangent line is horizontal Y = 2x°(x- 3)°

A:

Q: 14. Find the equation of the line tangent to the graph of f(x) = 2x3-x + 1 at x = -1. %3D

A:

Q: 18- What is equation of the tangent line of ƒ(x)=x³- 2x² - 1 at the point x = 2 ? y=-2x+9 1903…

A:

Q: 5. Find the equation of the tangent line for: x = vt + 9, y= at (4,-)

A: The objective is to find the equation of the tangent line.

Q: Find the length of the curve defined by y = 3 ln from x = 8 to x = 9.

A:

Q: 8. Find the point of the graph of f (x) = xe-2x where the tangent line is horizontal. %3D

A:

Q: 7) Find an equation of the line tangent to the curve y = x+5 at x = 3. х-1

A:

Q: The slope of the tangent line to the graph of the function y = 8VI - 4 at (16, 28) is O 1.50 O -1.75…

A: Given function is, y=8x-4

Q: The equation of the tangent line to the graph of f(x) = vx+1 At the indicated point (3,2) is:…

A: The given function is fx=x+1. Evaluate the slope of the function at the point (3, 2) as follows.…

Q: The tangent lines to the graph of f(x) = x2 grow steeper as x increases. At what rate do the slopes…

A: The tangent line of any given function is the line which  touches the curve of function at only one…

Q: If the instantaneous rate of change of g(x) at (-1, -2) is 1/2, write the equation of the line…

A:

Q: If the instantaneous rate of change of g(x) at (−1, −3) is 1/2, write the equation of the line…

A: Slope of tangent line is ½. So the equation is of the form:

Q: Find the points on the graph of y = ex + e-2x where the tangent line is horizontal.

A:

Q: 3. Determine the gradient of the tangent at a point (2, 5) to the XY graph with the implicit…

A:

Q: 3. Find an equation of the tangent line to the curve at x=4 y=(sqrt(x)) / (x+6)

A: Given equation of the curve y = xx+6  ...............(1) Let the equation of the tangent at (x1, y1)…

Q: Suppose that the second derivative of the function y = ƒ(x) is y′′ = (x + 1)(x - 2). For what…

A: For inflection point we must have y" = 0

Q: 6. Sketch the graph of y= x2+ by using the properties of the derivative.

A: The given function y=x2+2x

Q: 8) Find the equation of the tangent line to the graph of g(x) x3 7 at x = 2. -

A:

Q: Find an equation of the tangent line to the graph of the function at the given point. y = sinh(25 –…

A:

Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

A: The objective is to explain the reason definition of numerical derivative doesn't exist at x=2 in…

Q: 4) Determine the equation of the tangent line to the function 2 f(x) = x at the point (3, 9).

A:

Q: 7. Determine the equation of the tangent to the function E-2 f(x)=- at x= 1.

A:

Q: Find the equation of the line tangent to the graph of y = (x2 - x) ln (8x) at x = 2

A: Topic = Derivative

Q: The point on the graph of f(x) = 1 where the tangent line is parallel to the line 3z + y = 1 is: %3D

A:

Q: 4. Determine the equation of the tangent line to y = x²sin2x, at x = - R

A: Follow the procedure given below.

Q: 9. Find the equation of the curve whose y" e*. = - cos x + 6x + 4 with horizontal tangent at the…

A:

Q: 2) Find the tangent line to y2 = x at the point (4, –2).

A: Given: y2=x…

Q: Vehicle A is headed due west from a fixed point P at a rate of 45 miles/hour. Vehicle B is headed…

A:

Q: -1 Where on the curve Y (1+ x2)¯ does the tangent line have the greatest slope? NOTE: Enter the…

A: Given:- y = (1+x2)-1 To find:- Point where tangent line on given have greatest slope

Q: 4. If f (2) = 3 and f'(2) = 5, find an equation of the tangent line at the point where x=2.

A: We have to find the equation of tangent.

Q: Find the point where the tangent line to y = 5x at x = 0.5 crosses the x-axis.

A:

Q: Find the slope of the line tangent to the curve y = cos2 x at the point(−π/3 , 1/4)

A:

Q: The tangent lines to the graph of f (x) = x2 grow steeper as x increases. At what rate do the slopes…

A:

Q: 4. Find the equation for the tangent line to the graph of y = VT at a = 2. Remember to keep every…

A:

Q: So far, you've examined the function y = In x and its derivative, y' = , for large values of x. Now,…

A:

Q: 7) Find the equation of the tangent line to the graph of f(x) = –sin(x) +3 at x = 4

A:

Q: Find the equation of the line tangent to the graph ofy = 3 sin x + cos 2x at x = π/2

A:

Q: 4. Find the equation of the tangent line to the function y = In (x² – 2) when x=3.

A: Question is solved.