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

The tangent of y=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 y=5+5x^2-2x^3,\at x=a

tangent of

y = 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

y = 5 + 5 x^{2} - 2 x^{3} : \frac{d y}{d x} = - 6 x^{2} + 10 x

Compute the slope of

y = 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

\frac{d y}{d x} = \frac{4 sec ( y )}{( x + 6 ) ^{2}}

\frac{d}{d x} (\frac{e ^{x}}{2 x ^{2} + 5})

\int_{- 1}^{1} 2 d x

b \to 0 lim (\frac{b}{x ^{2} + b ^{2}})

n = 3 \sum \infty \frac{4 ^{n} + 1}{n !}

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