# What is the equation of the line normal to # f(x)=e^(sqrtx/x)# at # x=4#?

The normal line is perpendicular to the tangent line. So, if we use the derivative of the function to find the slope of the tangent line, we can then find the slope of the normal line and write its equation.

To find the derivative, first simplify the function:

And from here use the power rule:

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

To find the equation of the line normal to the function f(x) = e^(sqrt(x)/x) at x = 4, we need to determine the slope of the normal line and the point of tangency.

First, we find the derivative of f(x) with respect to x: f'(x) = (1 - sqrt(x))/(x^2 * e^(sqrt(x)/x))

Next, we substitute x = 4 into f'(x) to find the slope of the tangent line at x = 4: f'(4) = (1 - sqrt(4))/(4^2 * e^(sqrt(4)/4))

Simplifying this expression, we get: f'(4) = (1 - 2)/(16 * e^(1/2))

Now, we can find the slope of the normal line by taking the negative reciprocal of the slope of the tangent line: m_normal = -1/f'(4)

Finally, we have the slope of the normal line. To find the equation of the line, we also need a point on the line. Since the line is normal to the function at x = 4, we can use the coordinates (4, f(4)) as the point.

Substituting the values into the point-slope form of a line equation, we get: y - f(4) = m_normal * (x - 4)

Simplifying this equation will give us the final equation of the line normal to f(x) at x = 4.

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 derivative using limits of #f(x)=3x+2#?
- What is the slope of the line normal to the tangent line of #f(x) = x-sqrt(x^2+4) # at # x= 2 #?
- How do you find the equation of a line tangent to the function #y=3x-4sqrtx# at x=4?
- Find the antiderivative of f'(x)=3x^3?
- How do you use the definition of a derivative to find the derivative of #f(x) = sqrtx + 2# to calculate f'(2)?

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