What is the tangent of 4/3 x^3-7x+5 ?

The tangent of 4/3 x^3-7x+5 is y=(4a_{0}^2-7)x-8/3 a_{0}^3+5

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tangent of 4/3 x^3-7x+5

tangent of

\frac{4}{3} x^{3} - 7 x + 5

y = (4 a_{0}^{2} - 7) x - \frac{8}{3} a_{0}^{3} + 5

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{4}{3} a_{0}^{3} - 7 a_{0} + 5)

Find the slope of

y = \frac{4}{3} x^{3} - 7 x + 5 : \frac{d y}{d x} = 4 x^{2} - 7

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = 4 a_{0}^{2} - 7

Find the line with slope m=

4 a_{0}^{2} - 7

and passing through

(a_{0}, \frac{4}{3} a_{0}^{3} - 7 a_{0} + 5) : y = (4 a_{0}^{2} - 7) x - \frac{8}{3} a_{0}^{3} + 5

y = (4 a_{0}^{2} - 7) x - \frac{8}{3} a_{0}^{3} + 5

\int_{0}^{2} arctan (\frac{x}{2}) d x

\int \frac{10}{1 + x ^{2}} d x

x \to 0 lim (\frac{arcsin ( 2 x ) - 2 arcsin ( x )}{x ^{3}})

f (x) = x^{2}

x \to 3 lim (\frac{x - 2}{x + 5})

What is the tangent of 4/3 x^3-7x+5 ?
The tangent of 4/3 x^3-7x+5 is y=(4a_{0}^2-7)x-8/3 a_{0}^3+5