# How do you find the equation of a line tangent to the function #y=x^2+3x-1# at x=0?

- the gradient of the tangent at the given point is found by differentiating.

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

To find the equation of a line tangent to a function at a specific point, you need to find the derivative of the function and evaluate it at the given x-value.

The derivative of the function y = x^2 + 3x - 1 is y' = 2x + 3.

To find the slope of the tangent line at x = 0, substitute x = 0 into the derivative: y'(0) = 2(0) + 3 = 3.

Since the slope of the tangent line is 3, and it passes through the point (0, f(0)), which is (0, -1) in this case, you can use the point-slope form of a linear equation to find the equation of the tangent line.

Using the point-slope form, the equation of the tangent line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.

Plugging in the values, the equation of the tangent line is y - (-1) = 3(x - 0), which simplifies to y + 1 = 3x.

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)=1/(x-1)#?
- What is the equation of the normal line of #f(x)= 2(x-2)^4+(x-1)^3+(x-3)^2# at #x=4#?
- How to find instantaneous rate of change for #x^3 +2x^2 + x# at x from 1 to 2?
- How do you find the average rate of change of #f(x) = x^4 + 3x^3 - 5x^2 + 2x - 2# over the interval [-1,1]?
- How do you use the limit definition of the derivative to find the derivative of #f(x)=x^3+2x#?

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