# What is the equation of the normal line of #f(x)= x^e*e^x # at #x=3#?

First, find the point the normal line will intercept.

To find the slope of the normal line, we should first find the derivative of the function. This can be found through the product rule:

Thus,

By signing up, you agree to our Terms of Service and Privacy Policy

To find the equation of the normal line to the function f(x) = x^e * e^x at x = 3, we need to determine the slope of the tangent line at x = 3 and then find the negative reciprocal of that slope to obtain the slope of the normal line.

First, we find the derivative of f(x) using the product rule and the chain rule:

f'(x) = (e * x^(e-1) * e^x) + (x^e * e^x)

Next, we evaluate f'(x) at x = 3 to find the slope of the tangent line:

f'(3) = (e * 3^(e-1) * e^3) + (3^e * e^3)

Finally, we take the negative reciprocal of f'(3) to obtain the slope of the normal line. Let's call this slope m:

m = -1 / f'(3)

Therefore, the equation of the normal line to f(x) = x^e * e^x at x = 3 is given by:

y - f(3) = m(x - 3)

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the equation of a line tangent to #y=3x^2-x+4# at x=0?
- How do I use the limit definition of derivative to find #f'(x)# for #f(x)=mx+b# ?
- What is the equation of the line normal to # f(x)=xtanx# at # x=pi/3#?
- How do you find f'(x) using the limit definition given # (1/x^2) #?
- What is the instantaneous rate of change of #f(x)=1/(2x-5)# at #x=1 #?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7