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

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

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

tangent of

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

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

Solution steps

Find the tangent point:

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

Find the slope of

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

Compute the slope of

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

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

x \to 0 lim (\frac{3}{1 + x})

\frac{d}{d x} (x + sin^{2} (x))

(2 x y + x^{2} + x^{4}) d x - (1 + x^{2}) d y = 0

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

35.4 cos (0.1 (x + 6.2))

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