# How do you find the equation of the line that is tangent to #f(x)=x^3# and parallel to the line #3x-y+1=0#?

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

To find the equation of the line that is tangent to f(x)=x^3 and parallel to the line 3x-y+1=0, we need to determine the slope of the tangent line.

The slope of the given line can be found by rearranging it into slope-intercept form (y = mx + b), where m represents the slope.

3x - y + 1 = 0 -y = -3x - 1 y = 3x + 1

Therefore, the slope of the given line is 3.

Since the tangent line we are looking for is parallel to this line, it will have the same slope.

The derivative of f(x) = x^3 can be found by applying the power rule, which states that the derivative of x^n is n*x^(n-1).

f'(x) = 3x^2

To find the slope of the tangent line at a specific point on the curve, we substitute the x-coordinate of that point into the derivative. In this case, we want the tangent line to be parallel, so we can use any x-coordinate.

Let's choose x = 1.

f'(1) = 3(1)^2 f'(1) = 3

Therefore, the slope of the tangent line to f(x) = x^3 at x = 1 is 3.

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the tangent line.

The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) represents a point on the line and m is the slope.

We already have the slope, which is 3, and we know that the tangent line passes through the point (1, f(1)).

Substituting these values into the point-slope form, we get:

y - f(1) = 3(x - 1)

Simplifying further will give us the equation of the tangent line.

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 tangent and normal line to the curve #y=1+x^(2/3)# at (0,1)?
- How do you find the average rate of change of # f(x)=x^2-2x# from 1 to 5?
- How do you find the average rate of change of the function #F(x)=x^2-6x+5# over the interval [-2, -2+h]?
- At which point(s) does the graph of the function #f(x) = (x^2) / (x - 1)# have a horizontal tangent line?
- How do you find the equation of a line tangent to the function #y=-2tanx# at (-pi,0)?

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