16л The point P(1, 0) lies on the curve y = sin (a) If Q is the point (x, sin( 10), find the slope of the secant line PQ (correct to four decimal places) for the following values of x. (i) 2 (ii) 1.5 (iii) 1.4 (iv) 1.3 (v) 1.2
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Q: 6. Find the equation of the tangent line to the curve r* - a*y" = 12 at the point (-2, 1).
A: the equation of the tangent ( x0, y0 ) to the curve y=f(x) is y – y0 = f ′(x0)(x – x0)
Q: II FIND THE EQUATION OF THE TANGENT LINE AND NORMAL LINE TO THE FF. CURVES AT THE INDICATED POINT.…
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Q: 6. Consider the curve defined by 2x² + 3y² – 4xy = 36. | (a) Show that dx dy 2y – 2x Зу — 2х | (b)…
A: NOTE: As per our guidelines we are suppose to answer only 3 sub - parts.
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Q: 12. What is the equation of the tangent line to the curve y = x² – 2x + 1 at point (3,4)? a. у%3D 2х…
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Q: 14. Find the point(s) of the tangent to the curve h(x) x3 5x2 – 8x + 3 with same slope 3 4 as 48x +…
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- Inconclusive tests Show that the Second Derivative Test is inconclusive when applied to the following functions at (0, 0). Describe the behavior of the function at (0, 0). ƒ(x, y) = sin (x2y2)slope of the line tangent to the curve cos(5x-4y)-x(e^-x)=(-7pi/2)*(e^(-7pi/2))at the point (7pi/2,3pi)Tangent lines Find an equation of the line tangent to the cycloidx = t - sin t, y = 1 - cos t at the points corresponding to t = π/6 and t = 2π/3.
- (a) Applications of partial derivative: ii) A bee was flying upward along the curve that is the section ofz = x^4 + xy^3 + 12 with the plane x = 1. At the point (1, -2, 5), it went off on the tangent line. Where did the bee hit the xz-planeFind the values of h, k, and a that make the circle (x - h)2 + (y - k)2 = a2 tangent to the parabola y = x2 + 1 at the point (1, 2) and that also make the second derivatives d2y/dx2 have the same value on both curves there. Circles like this one that are tangent to a curve and have the same second derivative as the curve at the point of tangency are called osculating circles.Inconclusive tests Apply the Second Derivative Test to the followingfunctions and interpret the results.a. ƒ(x, y) = 2x4 + y4 b. ƒ(x, y) = 2 - xy2
- Derivatives from tangent lines Suppose the line tangent to thegraph of f at x = 2 is y = 4x + 1 and suppose y = 3x - 2 isthe line tangent to the graph of g at x = 2. Find an equation of theline tangent to the following curves at x = 2.a. y = f(x)g(x) b. y = f(x)/g(x)parametric 2 Determine the slope of the tangent line to the curve x( t )=2 t3 −7 t2 +9 t +3 y( t )=7 e2 t−2 at the point where t=1 and determine the equation of the tangent line to the curve at the point where t=1. [(dy)/(dx)] = y ( x ) =Find an equation of the tangent line to the graph of the function f through the point (x0, y0) not on the graph. To find the point of tangency (x, y) on the graph of f, solve the equation f′(x) = (y0 − y)/(x0 − x) f(x) = 2/x (x0, y0) = (5, 0)
- The curve y = f (x) passes through the point A(1; 2). Each tangent at any point M(x,y) on the curve intersects the straight line y = 1 at a point whose x coordinate is twice the x coordinate of point M. Determine the equation of the curve.The equation of tangent as we know (y-y0)=m(x-x0) m is the slop at (x0,y0), find the equation of tangent for the function x^2 +2xy-y^2+x =2. at the point (1,2).Captionless Image(x) = cos x − 8x , [0, 4π] Find all relative extrema of the function. Use the Second Derivative Test where applicable. What is the relative minimum and maximum?