# How do you find the tangent line to the curve #y=x^3-9x# at the point where #x=1#?

Given:

Let

So, the point we are targeting is

To find the slope of the tangent line there, we must differentiate

At

So, the slope of the tangent line is

Now, we use the point-slope formula to compute the equation, that is,

#(x_0,y_0)# are the original coordinates

Therefore, we get,

A graph shows it:

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

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

To find the tangent line to the curve y=x^3-9x at the point where x=1, we need to find the slope of the curve at that point.

First, we find the derivative of the function y=x^3-9x with respect to x. The derivative of x^3 is 3x^2, and the derivative of -9x is -9. Therefore, the derivative of the function is dy/dx = 3x^2 - 9.

Next, we substitute x=1 into the derivative to find the slope at that point. dy/dx = 3(1)^2 - 9 = -6.

The slope of the tangent line is -6.

To find the equation of the tangent line, we use the point-slope form of a line. The equation is y - y1 = m(x - x1), where (x1, y1) is the point on the curve where x=1, and m is the slope.

Substituting x=1 and y=1^3-9(1) into the equation, we have y - (-8) = -6(x - 1).

Simplifying, we get y + 8 = -6x + 6.

Rearranging the equation, we have y = -6x - 2.

Therefore, the equation of the tangent line to the curve y=x^3-9x at the point where x=1 is y = -6x - 2.

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

- What is the equation of the tangent line of #f(x) = 4/(x-1)# at #x=0#?
- For #f(x)=x^5-x^3+x# what is the equation of the tangent line at #x=3#?
- How do you find the equation of tangent line to the curve #(2x+3)^(1/2)# at the point x=3?
- Find an equation of the tangent line to the curve at the given point ? y= (sqrt x) , (49,7)
- How do you find the derivative of #f(x) = 3/(x-2)# using the limit definition?

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