25-32 Use implicit differentiation to find an equation of the tangent line to the curve at the given point. 28. x² + 2xy + 4y² = 12, (2, 1) (ellipse)
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- a.) Find an equation of the tangent line to the curve at the given point. y = (4)/(sinx + cosx), P = (0, 4) b.) Find an equation of the tangent line to the curve at the given point. y = 4x + 2 cos(x), P = (0, 2)1. Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2 + y2 = (3x2 + 4y2 − x)2 (0, 0.25) (cardioid) 2. Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 + y2/3 = 4 (−3, √ 3, 1) (astroid)(a) The curve with equation y2 = x3 + 3x2 is called the Tschirnhausen cubic. Find an equation of the tangent line to this curve at the point (1, 2). y = (b) At what points does this curve have horizontal tangents? (x,y) ( ) smaller y value (x,y) ( ) larger y value
- The function y = sin x completes one period on the interval 30, 2π4, the function y = sin 2x completes two periods, the function y = sin (x/2) completes half a period, and so on. Is there any relation between the number of periods y = sin mx completes on 30, 2π4 and the slope of the curve y = sin mx at the origin? Give reasons for your answer.(Differentiation) 6.1.7.2) Find Tangent equation of a curve (Ans. y = 2x - 3)Find the equation of the tangent line to the curve y=5x /1+x^2 at the point (4, 20/17) The equation of this tangent line can be written in the form y=mx+b.The equation of the tangent line is y=