# How do you find the equation of the tangent line to the curve #f(x) = x^2 + 2x#; at x=3, x=5?

Tangent at

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

To find the equation of the tangent line to the curve f(x) = x^2 + 2x at x=3 and x=5, we need to find the slope of the tangent line at those points and then use the point-slope form of a line to write the equation.

To find the slope of the tangent line at a given point, we can use the derivative of the function. Taking the derivative of f(x) = x^2 + 2x, we get f'(x) = 2x + 2.

At x=3, the slope of the tangent line is f'(3) = 2(3) + 2 = 8.

At x=5, the slope of the tangent line is f'(5) = 2(5) + 2 = 12.

Using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can write the equations of the tangent lines.

At x=3, the equation of the tangent line is y - f(3) = 8(x - 3).

At x=5, the equation of the tangent line is y - f(5) = 12(x - 5).

Simplifying these equations will give the final equations of the tangent lines.

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 average rate of change of #f(x) = 1/x+6# from [2,2+h]?
- A ladder is leaning against a wall, and the floor and slipping. If the bottom of the ladder is slipping at #30 cms^(-1)# then how fast is the top of the ladder sliding down the wall when the ladder is at #45^o#?
- Does every point on a continuous function have a tangent line?
- How do you find the instantaneous rate of change for #f(x) = 3/x # for x=2?
- How do you find the equation of a line tangent to a graph #f(x)=x(1-2x)^3# at the point (1,-1) is?

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