What is the tangent of y=8x^4,\at x=2 ?

The tangent of y=8x^4,\at x=2 is y=256x-384

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tangent of y=8x^4,\at x=2

tangent of

y = 8 x^{4}, at x = 2

y = 256 x - 384

Solution steps

Find the tangent point:

(2, 128)

Find the slope of

y = 8 x^{4} : \frac{d y}{d x} = 32 x^{3}

Compute the slope of

y = 8 x^{4}

x = 2 : m = 256

Find the line with slope m=

256

and passing through

(2, 128) : y = 256 x - 384

y = 256 x - 384

f (x) = (x^{3} - 4 x)^{8}, at x = 2

f (x) = 3^{2 x}

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

\int 2 x^{2} 1 - x^{3} d x

\frac{\partial}{\partial x} (3 x y + y^{2})

What is the tangent of y=8x^4,\at x=2 ?
The tangent of y=8x^4,\at x=2 is y=256x-384