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

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

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

normal of

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

y = - \frac{1}{4} x + 4

Solution steps

Find the slope of

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

Compute the slope of

y = x^{4} + 4 e^{x}

(0, 4) : m = 4

Compute the slope of the perpendicular line:

m_{p} = - \frac{1}{4}

Find the line with slope m=

- \frac{1}{4}

and passing through

(0, 4) : y = - \frac{1}{4} x + 4

y = - \frac{1}{4} x + 4

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