What is the tangent of f(x)=x^3,a ?

The tangent of f(x)=x^3,a is y=3a^2x-2a^3

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tangent of f(x)=x^3,a

tangent of

f (x) = x^{3}, a

y = 3 a^{2} x - 2 a^{3}

Solution steps

Compute the tangent line to the general point

x = a

Find the tangent point:

(a, a^{3})

Find the slope of

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

Compute the slope of

f (x) = x^{3}

x = a : m = 3 a^{2}

Find the line with slope m=

3 a^{2}

and passing through

(a, a^{3}) : y = 3 a^{2} x - 2 a^{3}

y = 3 a^{2} x - 2 a^{3}

\int (13 x + 11) d x

\int - 3 x \cdot e^{- 3 x} d x

x \to - 3 lim (25)

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

x \to 4 lim (x + 2)