# How do you find the linearization of #f(x) = sqrt(x)# at x=49?

The linearization is the equation of the tangent line.

The tangent line is

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

To find the linearization of ( f(x) = \sqrt{x} ) at ( x = 49 ), follow these steps:

- Calculate the derivative of ( f(x) ) using the power rule: ( f'(x) = \frac{1}{2\sqrt{x}} ).
- Evaluate the derivative at ( x = 49 ) to find the slope of the tangent line: ( f'(49) = \frac{1}{2\sqrt{49}} = \frac{1}{14} ).
- Use the point-slope form of a line ( y - y_1 = m(x - x_1) ), where ( m ) is the slope and ( (x_1, y_1) ) is a point on the line. Substitute ( m = \frac{1}{14} ) and ( (x_1, y_1) = (49, \sqrt{49}) ).
- Simplify to obtain the linearization: ( y - \sqrt{49} = \frac{1}{14}(x - 49) ).
- Optionally, simplify further: ( y = \frac{1}{14}x + 3 ).

Therefore, the linearization of ( f(x) = \sqrt{x} ) at ( x = 49 ) is ( y = \frac{1}{14}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.

- A street light is mounted at the top of a 15ft tall pole. A man 6ft tall walks away from the pole with a speed of 5ft/sec along a straight path. How fast is the tip of his shadow moving when he is 40ft from the pole?
- How do you find the dimensions of a rectangle with area 1000 m whose perimeter is as small as possible?
- A hypothetical cube shrinks at a rate of 8 m³/min. At what rate are the sides of the cube changing when the sides are 3 m each?
- A farmer wants to fence an area of 6 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. How can he do this so as to minimize the cost of the fence?
- How do you find the linearization at a=1 of #f(x) = ln(x)#?

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