What is the tangent of f(x)=((x^2+7)(5-x)) ?

The tangent of f(x)=((x^2+7)(5-x)) is y=(10a_{0}-3a_{0}^2-7)x+2a_{0}^3-5a_{0}^2+35

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tangent of f(x)=((x^2+7)(5-x))

tangent of

f (x) = ((x^{2} + 7) (5 - x))

y = (10 a_{0} - 3 a_{0}^{2} - 7) x + 2 a_{0}^{3} - 5 a_{0}^{2} + 35

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, (a_{0}^{2} + 7) (5 - a_{0}))

Find the slope of

f (x) = (x^{2} + 7) (5 - x) : \frac{df ( x )}{d x} = 10 x - 3 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 = 10 a_{0} - 3 a_{0}^{2} - 7

Find the line with slope m=

10 a_{0} - 3 a_{0}^{2} - 7

and passing through

(a_{0}, (a_{0}^{2} + 7) (5 - a_{0})) : y = (10 a_{0} - 3 a_{0}^{2} - 7) x + 2 a_{0}^{3} - 5 a_{0}^{2} + 35

y = (10 a_{0} - 3 a_{0}^{2} - 7) x + 2 a_{0}^{3} - 5 a_{0}^{2} + 35

\frac{\partial}{\partial x} (e^{x - y})

\frac{x - 4}{x}

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

y = 2 sin (3 x)

x \to 0 lim (x cos (\frac{6}{x}))

What is the tangent of f(x)=((x^2+7)(5-x)) ?
The tangent of f(x)=((x^2+7)(5-x)) is y=(10a_{0}-3a_{0}^2-7)x+2a_{0}^3-5a_{0}^2+35