What is the tangent of f(x)=7+4x^2-2x^3,\at x=a ?

The tangent of f(x)=7+4x^2-2x^3,\at x=a is y=(-6a^2+8a)x+4a^3-4a^2+7

tangent of f(x)=7+4x^2-2x^3,\at x=a

tangent of

f (x) = 7 + 4 x^{2} - 2 x^{3}, at x = a

y = (- 6 a^{2} + 8 a) x + 4 a^{3} - 4 a^{2} + 7

Solution steps

Find the tangent point:

(a, 7 + 4 a^{2} - 2 a^{3})

Find the slope of

f (x) = 7 + 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, 7 + 4 a^{2} - 2 a^{3}) : y = (- 6 a^{2} + 8 a) x + 4 a^{3} - 4 a^{2} + 7

y = (- 6 a^{2} + 8 a) x + 4 a^{3} - 4 a^{2} + 7

d er i v a t i v e 4 e^{x^{- 3}}

x \to 0 lim (9 x^{2} - 4 x + 8)

\int sec^{2} (x) d x

y^{^{''}} + 1.5 y^{^{'}} + 0.037 y = 0, y (0) = 2, y^{^{'}} (0) = 1

\frac{d}{d x} (3^{x} + 5)

What is the tangent of f(x)=7+4x^2-2x^3,\at x=a ?
The tangent of f(x)=7+4x^2-2x^3,\at x=a is y=(-6a^2+8a)x+4a^3-4a^2+7