What is the tangent of f(x)=3+4x^2-2x^3,\at x=a ?

The tangent of f(x)=3+4x^2-2x^3,\at x=a is y=(-6a^2+8a)x+4a^3-4a^2+3

tangent of f(x)=3+4x^2-2x^3,\at x=a

tangent of

f (x) = 3 + 4 x^{2} - 2 x^{3}, at x = a

y = (- 6 a^{2} + 8 a) x + 4 a^{3} - 4 a^{2} + 3

Solution steps

Find the tangent point:

(a, 3 + 4 a^{2} - 2 a^{3})

Find the slope of

f (x) = 3 + 4 x^{2} - 2 x^{3} : \frac{df ( x )}{d x} = - 6 x^{2} + 8 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} + 8 a

Find the line with slope m=

- 6 a^{2} + 8 a

and passing through

(a, 3 + 4 a^{2} - 2 a^{3}) : y = (- 6 a^{2} + 8 a) x + 4 a^{3} - 4 a^{2} + 3

y = (- 6 a^{2} + 8 a) x + 4 a^{3} - 4 a^{2} + 3

(y + 4) y^{^{'}} = 2 x y + 4 y, y (2) = 1

\int (1 + 30 w) w d w

d er i v a t i v e f (x) = 6 x + 8

d er i v a t i v e e^{3 - x}

d er i v a t i v e f (x) = 2^{4 x} + 4 x^{2}

What is the tangent of f(x)=3+4x^2-2x^3,\at x=a ?
The tangent of f(x)=3+4x^2-2x^3,\at x=a is y=(-6a^2+8a)x+4a^3-4a^2+3