What is the tangent of y=(x^2)/2+4x+2,(-3,-11/2) ?

The tangent of y=(x^2)/2+4x+2,(-3,-11/2) is y=x-5/2

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tangent of y=(x^2)/2+4x+2,(-3,-11/2)

tangent of

y = \frac{x ^{2}}{2} + 4 x + 2, (- 3, - \frac{11}{2})

y = x - \frac{5}{2}

Solution steps

Find the slope of

y = \frac{x ^{2}}{2} + 4 x + 2 : \frac{d y}{d x} = x + 4

Compute the slope of

y = \frac{x ^{2}}{2} + 4 x + 2

(- 3, - \frac{11}{2}) : m = 1

Find the line with slope m=

1

and passing through

(- 3, - \frac{11}{2}) : y = x - \frac{5}{2}

y = x - \frac{5}{2}

y^{^{'}} + \frac{1}{2} y = y^{3}

\frac{1}{2} e^{- t} cos (t) + \frac{1}{2} e^{- t} sin (t) - \frac{1}{2} e^{- 2 t}

\frac{d}{d x} (cos^{2} (ln (x)))

y^{^{''}} + 8 y^{^{'}} + 6 y = 0

\frac{4 s + 3}{s ( s ^{2} + 6 s + 34 )}

What is the tangent of y=(x^2)/2+4x+2,(-3,-11/2) ?
The tangent of y=(x^2)/2+4x+2,(-3,-11/2) is y=x-5/2