What is the tangent of f(x)=x^4+9e^x,\at x=0 ?

The tangent of f(x)=x^4+9e^x,\at x=0 is y=9x+9

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tangent of f(x)=x^4+9e^x,\at x=0

tangent of

f (x) = x^{4} + 9 e^{x}, at x = 0

y = 9 x + 9

Solution steps

Find the tangent point:

(0, 9)

Find the slope of

f (x) = x^{4} + 9 e^{x} : \frac{df ( x )}{d x} = 4 x^{3} + 9 e^{x}

Compute the slope of

f (x) = x^{4} + 9 e^{x}

x = 0 : m = 9

Find the line with slope m=

9

and passing through

(0, 9) : y = 9 x + 9

y = 9 x + 9

\int \frac{x ^{2}}{2 ^{x}} d x

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

\int \frac{x ^{2} + 5}{x} d x

\frac{x ^{2}}{5 + x}

What is the tangent of f(x)=x^4+9e^x,\at x=0 ?
The tangent of f(x)=x^4+9e^x,\at x=0 is y=9x+9