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Popular >

tangent of f(x)=x-x^3

Solution

tangent of

f (x) = x - x^{3}

Solution

y = (1 - 3 a_{0}^{2}) x + 2 a_{0}^{3}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0} - a_{0}^{3})

Find the slope of

f (x) = x - x^{3} : \frac{df ( x )}{d x} = 1 - 3 x^{2}

Compute the slope of

f (x) = x - x^{3}

at

x = a_{0} : m = 1 - 3 a_{0}^{2}

Find the line with slope m=

1 - 3 a_{0}^{2}

and passing through

(a_{0}, a_{0} - a_{0}^{3}) : y = (1 - 3 a_{0}^{2}) x + 2 a_{0}^{3}

y = (1 - 3 a_{0}^{2}) x + 2 a_{0}^{3}

Popular Examples

integral of ln(y)+4xy^3

\int ln (y) + 4 x y^{3} d x

derivative of 4x-x^2y+y^3

\frac{d}{d x} (4 x - x^{2} y + y^{3})

inverse oflaplace (s+3)/(s^2+4s+5)inverse laplace

\frac{s + 3}{s ^{2} + 4 s + 5}

integral of (11)/(2xsqrt(4x^2-16))

\int \frac{11}{2 x 4 x ^{2} - 16} d x

integral of ((ax+b))/((cx+)

\int \frac{( a x + b )}{( c x + d )} d x

Frequently Asked Questions (FAQ)

What is the tangent of f(x)=x-x^3 ?
The tangent of f(x)=x-x^3 is y=(1-3a_{0}^2)x+2a_{0}^3