What is the tangent of 100x^2+400x+5000,0.5 ?

The tangent of 100x^2+400x+5000,0.5 is y=(200a_{0}+400)x-100a_{0}^2+5000

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tangent of 100x^2+400x+5000,0.5

tangent of

100 x^{2} + 400 x + 5000, 0.5

y = (200 a_{0} + 400) x - 100 a_{0}^{2} + 5000

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 100 a_{0}^{2} + 400 a_{0} + 5000)

Find the slope of

y = 100 x^{2} + 400 x + 5000 : \frac{d y}{d x} = 200 x + 400

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 = 200 a_{0} + 400

Find the line with slope m=

200 a_{0} + 400

and passing through

(a_{0}, 100 a_{0}^{2} + 400 a_{0} + 5000) : y = (200 a_{0} + 400) x - 100 a_{0}^{2} + 5000

y = (200 a_{0} + 400) x - 100 a_{0}^{2} + 5000

What is the tangent of 100x^2+400x+5000,0.5 ?
The tangent of 100x^2+400x+5000,0.5 is y=(200a_{0}+400)x-100a_{0}^2+5000