What is the tangent of-1/2 x^2-2x+3 ?

The tangent of-1/2 x^2-2x+3 is y=(-a_{0}-2)x+1/2 a_{0}^2+3

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tangent of-1/2 x^2-2x+3

tangent

y = (- a_{0} - 2) x + \frac{1}{2} a_{0}^{2} + 3

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, - \frac{1}{2} a_{0}^{2} - 2 a_{0} + 3)

Find the slope of

y = - \frac{1}{2} x^{2} - 2 x + 3 : \frac{d y}{d x} = - x - 2

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = - a_{0} - 2

Find the line with slope m=

- a_{0} - 2

and passing through

(a_{0}, - \frac{1}{2} a_{0}^{2} - 2 a_{0} + 3) : y = (- a_{0} - 2) x + \frac{1}{2} a_{0}^{2} + 3

y = (- a_{0} - 2) x + \frac{1}{2} a_{0}^{2} + 3

What is the tangent of-1/2 x^2-2x+3 ?
The tangent of-1/2 x^2-2x+3 is y=(-a_{0}-2)x+1/2 a_{0}^2+3