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

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

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tangent of f(x)=6+5x^2-2x^3,\at x=a

tangent of

f (x) = 6 + 5 x^{2} - 2 x^{3}, at x = a

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

Solution steps

Find the tangent point:

(a, 6 + 5 a^{2} - 2 a^{3})

Find the slope of

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

Compute the slope of

f (x) = 6 + 5 x^{2} - 2 x^{3}

x = a : m = - 6 a^{2} + 10 a

Find the line with slope m=

- 6 a^{2} + 10 a

and passing through

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

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

\frac{d}{d t} (e^{- 8 t})

\frac{5}{( s + 1 ) ( s + 2 ) ^{2}}

cos (3 \cdot x) \cdot cos (5 \cdot x)

\frac{\partial}{\partial y} (e^{(\frac{x}{y})})

\frac{d}{d x} (7^{9 x})

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