What is the tangent of f(x)=x^3-1.5x^2-90x-22 ?

The tangent of f(x)=x^3-1.5x^2-90x-22 is y=(3a_{0}^2-3a_{0}-90)x+(-4a_{0}^3+3a_{0}^2-44)/2

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tangent of f(x)=x^3-1.5x^2-90x-22

tangent of

f (x) = x^{3} - 1.5 x^{2} - 90 x - 22

y = (3 a_{0}^{2} - 3 a_{0} - 90) x + \frac{- 4 a _{0}^{3} + 3 a _{0}^{2} - 44}{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{3} - 1.5 a_{0}^{2} - 90 a_{0} - 22)

Find the slope of

f (x) = x^{3} - 1.5 x^{2} - 90 x - 22 : \frac{df ( x )}{d x} = 3 x^{2} - 3 x - 90

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 = 3 a_{0}^{2} - 3 a_{0} - 90

Find the line with slope m=

3 a_{0}^{2} - 3 a_{0} - 90

and passing through

(a_{0}, a_{0}^{3} - 1.5 a_{0}^{2} - 90 a_{0} - 22) : y = (3 a_{0}^{2} - 3 a_{0} - 90) x + \frac{- 4 a _{0}^{3} + 3 a _{0}^{2} - 44}{2}

y = (3 a_{0}^{2} - 3 a_{0} - 90) x + \frac{- 4 a _{0}^{3} + 3 a _{0}^{2} - 44}{2}

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What is the tangent of f(x)=x^3-1.5x^2-90x-22 ?
The tangent of f(x)=x^3-1.5x^2-90x-22 is y=(3a_{0}^2-3a_{0}-90)x+(-4a_{0}^3+3a_{0}^2-44)/2