What is the normal of f(x)=x^4+2e^x,(0,2) ?

The normal of f(x)=x^4+2e^x,(0,2) is f(x)=-1/2 x+2

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normal of f(x)=x^4+2e^x,(0,2)

normal of

f (x) = x^{4} + 2 e^{x}, (0, 2)

f (x) = - \frac{1}{2} x + 2

Solution steps

Find the slope of

f (x) = x^{4} + 2 e^{x} : \frac{df ( x )}{d x} = 4 x^{3} + 2 e^{x}

Compute the slope of

f (x) = x^{4} + 2 e^{x}

(0, 2) : m = 2

Compute the slope of the perpendicular line:

m_{p} = - \frac{1}{2}

Find the line with slope m=

- \frac{1}{2}

and passing through

(0, 2) : f (x) = - \frac{1}{2} x + 2

f (x) = - \frac{1}{2} x + 2

(sin (x))^{2}

x \to 0 + lim (- x + 5)

e^{- 3 x}

x \to 9 - lim (\frac{x ^{9}}{x - 9})

x \to 0 + lim (x ln (x^{6}))

What is the normal of f(x)=x^4+2e^x,(0,2) ?
The normal of f(x)=x^4+2e^x,(0,2) is f(x)=-1/2 x+2