What is the tangent of f(x)=2x(2-4x)^4,\at x=1 ?

The tangent of f(x)=2x(2-4x)^4,\at x=1 is y=288x-256

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tangent of f(x)=2x(2-4x)^4,\at x=1

tangent of

f (x) = 2 x (2 - 4 x)^{4}, at x = 1

y = 288 x - 256

Solution steps

Find the tangent point:

(1, 32)

Find the slope of

f (x) = 2 x (2 - 4 x)^{4} : \frac{df ( x )}{d x} = 2 ((2 - 4 x)^{4} - 16 x (2 - 4 x)^{3})

Compute the slope of

f (x) = 2 x (2 - 4 x)^{4}

x = 1 : m = 288

Find the line with slope m=

288

and passing through

(1, 32) : y = 288 x - 256

y = 288 x - 256

\int \frac{tan ^{2} ( x )}{sec ^{3} ( x )} d x

(t^{2} + 1) \frac{d y}{d t} = 2 y

\frac{\partial}{\partial x} (x^{8} + 8 x y^{7})

\int 1 d x^{3}

What is the tangent of f(x)=2x(2-4x)^4,\at x=1 ?
The tangent of f(x)=2x(2-4x)^4,\at x=1 is y=288x-256