What is the tangent of x^4+3e^x ?

The tangent of x^4+3e^x is y=(4a_{0}^3+3e^{a_{0}})x-3a_{0}^4-3a_{0}e^{a_{0}}+3e^{a_{0}}

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tangent of x^4+3e^x

tangent of

x^{4} + 3 e^{x}

y = (4 a_{0}^{3} + 3 e^{a_{0}}) x - 3 a_{0}^{4} - 3 a_{0} e^{a_{0}} + 3 e^{a_{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{4} + 3 e^{a_{0}})

Find the slope of

y = x^{4} + 3 e^{x} : \frac{d y}{d x} = 4 x^{3} + 3 e^{x}

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}^{3} + 3 e^{a_{0}}

Find the line with slope m=

4 a_{0}^{3} + 3 e^{a_{0}}

and passing through

(a_{0}, a_{0}^{4} + 3 e^{a_{0}}) : y = (4 a_{0}^{3} + 3 e^{a_{0}}) x - 3 a_{0}^{4} - 3 a_{0} e^{a_{0}} + 3 e^{a_{0}}

y = (4 a_{0}^{3} + 3 e^{a_{0}}) x - 3 a_{0}^{4} - 3 a_{0} e^{a_{0}} + 3 e^{a_{0}}

What is the tangent of x^4+3e^x ?
The tangent of x^4+3e^x is y=(4a_{0}^3+3e^{a_{0}})x-3a_{0}^4-3a_{0}e^{a_{0}}+3e^{a_{0}}