What is the normal of f(x)=x^4+5e^x,(0,5) ?

The normal of f(x)=x^4+5e^x,(0,5) is f(x)=-1/5 x+5

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normal of f(x)=x^4+5e^x,(0,5)

normal of

f (x) = x^{4} + 5 e^{x}, (0, 5)

f (x) = - \frac{1}{5} x + 5

Solution steps

Find the slope of

f (x) = x^{4} + 5 e^{x} : \frac{df ( x )}{d x} = 4 x^{3} + 5 e^{x}

Compute the slope of

f (x) = x^{4} + 5 e^{x}

(0, 5) : m = 5

Compute the slope of the perpendicular line:

m_{p} = - \frac{1}{5}

Find the line with slope m=

- \frac{1}{5}

and passing through

(0, 5) : f (x) = - \frac{1}{5} x + 5

f (x) = - \frac{1}{5} x + 5

f (x) = a x

\int_{- \infty}^{0} x \cdot e^{x} d x

\frac{d x}{d t} = x^{2} e^{- 2 t}

\int (\frac{3 - x}{x ^{2} - 6 x + 2}) d x

\frac{d}{d x} (cos (\frac{π x}{4}))

What is the normal of f(x)=x^4+5e^x,(0,5) ?
The normal of f(x)=x^4+5e^x,(0,5) is f(x)=-1/5 x+5