What is the tangent of f(x)=9x^2+7x-6 ?

The tangent of f(x)=9x^2+7x-6 is y=(18a_{0}+7)x-9a_{0}^2-6

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tangent of f(x)=9x^2+7x-6

tangent

y = (18 a_{0} + 7) x - 9 a_{0}^{2} - 6

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 9 a_{0}^{2} + 7 a_{0} - 6)

Find the slope of

f (x) = 9 x^{2} + 7 x - 6 : \frac{df ( x )}{d x} = 18 x + 7

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 = 18 a_{0} + 7

Find the line with slope m=

18 a_{0} + 7

and passing through

(a_{0}, 9 a_{0}^{2} + 7 a_{0} - 6) : y = (18 a_{0} + 7) x - 9 a_{0}^{2} - 6

y = (18 a_{0} + 7) x - 9 a_{0}^{2} - 6

What is the tangent of f(x)=9x^2+7x-6 ?
The tangent of f(x)=9x^2+7x-6 is y=(18a_{0}+7)x-9a_{0}^2-6