What is the normal of f(x)=3e^x+2x,(0,3) ?

The normal of f(x)=3e^x+2x,(0,3) is f(x)=-1/5 x+3

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normal of f(x)=3e^x+2x,(0,3)

normal of

f (x) = 3 e^{x} + 2 x, (0, 3)

f (x) = - \frac{1}{5} x + 3

Solution steps

Find the slope of

f (x) = 3 e^{x} + 2 x : \frac{df ( x )}{d x} = 3 e^{x} + 2

Compute the slope of

f (x) = 3 e^{x} + 2 x

(0, 3) : 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, 3) : f (x) = - \frac{1}{5} x + 3

f (x) = - \frac{1}{5} x + 3

x \to 0 lim (\frac{1}{x ^{3}})

x \to 0 + lim (x^{17 x})

\int_{0}^{5} x e^{- x^{2}} d x

\int x cos (118 x) d x

\int_{0}^{1} 9 x^{2} (1 - 5 x^{3})^{2} d x

What is the normal of f(x)=3e^x+2x,(0,3) ?
The normal of f(x)=3e^x+2x,(0,3) is f(x)=-1/5 x+3