What is the tangent of f(x)=9+5x^2-2x^3,\at x=a ?

The tangent of f(x)=9+5x^2-2x^3,\at x=a is y=(-6a^2+10a)x+4a^3-5a^2+9

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tangent of f(x)=9+5x^2-2x^3,\at x=a

tangent of

f (x) = 9 + 5 x^{2} - 2 x^{3}, at x = a

y = (- 6 a^{2} + 10 a) x + 4 a^{3} - 5 a^{2} + 9

Solution steps

Find the tangent point:

(a, 9 + 5 a^{2} - 2 a^{3})

Find the slope of

f (x) = 9 + 5 x^{2} - 2 x^{3} : \frac{df ( x )}{d x} = - 6 x^{2} + 10 x

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 = - 6 a^{2} + 10 a

Find the line with slope m=

- 6 a^{2} + 10 a

and passing through

(a, 9 + 5 a^{2} - 2 a^{3}) : y = (- 6 a^{2} + 10 a) x + 4 a^{3} - 5 a^{2} + 9

y = (- 6 a^{2} + 10 a) x + 4 a^{3} - 5 a^{2} + 9

What is the tangent of f(x)=9+5x^2-2x^3,\at x=a ?
The tangent of f(x)=9+5x^2-2x^3,\at x=a is y=(-6a^2+10a)x+4a^3-5a^2+9