?? Find the slope of the tangent line to the curve at the point (1, 2). Give an

Question

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Find the slope of the tangent line to the curve at the point (1, 2). Give an exact value. X^3 + 5x^2y + 2y^2 = 4y + 11 Consider the curve given by y = x/y + b. Find the slope of the tangent line to the curve at the point (0, 0). Your answer will have b in it. Find the equation of the tangent line to the curve at the point (0. 0}. Your answer will have o in it. Y(x) = Consider the curve defined by x^2 + y^2 - 3x + 13y = 14. Find dy/dx. Under what condition on x is the tangent line to the curve horizontal? The curve has a horizontal tangent line when dy/dx is zero, which occurs when x = Under what condition on y is the tangent line to the curve vertical? The curve has a vertical tangent line when dy/dx is undefined which occurs when

Explanation / Answer

1)given curve x3+5x2y +2y2=4y +11

differentiate with respect to x on both sides

3x2+(5*2xy +5x2y') +2*2yy'=4y' +0

3x2+10xy +5x2y' +4yy'=4y'

at x =1, y =2

(3*12)+(10*1*2) +(5*12y') +(4*2y')=4y'

3+20 +5y' +8y'=4y'

23+13y'=4y'

13y'-4y'=-23

9y'=-23

y'=-23/9

slope of tangent line to the curve at (1,2) is -23/9

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