# What is the slope of the line normal to the tangent line of #f(x) = 2x-4sqrt(x-1) # at # x= 2 #?

The slope will be undefined.

Start by finding the y-coordinate of the point of tangency.

Now find the slope of the tangent.

Hopefully this helps!

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

To find the slope of the line normal to the tangent line of the function f(x) = 2x - 4√(x - 1) at x = 2, we first need to find the slope of the tangent line. Then, we can find the negative reciprocal of this slope to get the slope of the normal line.

- Find the derivative of the function f(x) with respect to x.
- Evaluate the derivative at x = 2 to find the slope of the tangent line.
- Take the negative reciprocal of this slope to find the slope of the normal line.

Let's find the derivative of f(x):

f'(x) = d(2x - 4√(x - 1))/dx

To find the derivative of 2x, we get 2.

To find the derivative of -4√(x - 1), we apply the chain rule:

d/dx(√u) = (1/2√u) * du/dx

Here, u = (x - 1), so du/dx = 1.

Substitute u = (x - 1) and du/dx = 1:

d/dx(-4√(x - 1)) = -4 * (1/2√(x - 1)) * 1 = -2/√(x - 1)

So, f'(x) = 2 - 2/√(x - 1)

Now, evaluate f'(x) at x = 2:

f'(2) = 2 - 2/√(2 - 1) = 2 - 2/√1 = 2 - 2 = 0

The slope of the tangent line at x = 2 is 0.

The slope of the normal line is the negative reciprocal of the slope of the tangent line, so it is undefined.

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 the line tangent to #f(x) = x^3# at x = 2?
- How do you find the equation of a line tangent to the function #y=4x-x^2# at (2,4)?
- How do you find a function f(x), which, when multiplied by its derivative, gives you #x^3#, and for which #f(0) = 4#?
- How do you find the equation of the tangent to the curve defined by #y= (2e^x) / (1+e^x)# at the point (0,1)?
- How do you find the slope of the secant lines of #f(x)=x^3-12x+1# through the points: -3 and 3?

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