How do you find the equation of the tangent line to the curve #y=x^3 - 2x# at the point (2,4)?
#y=10x-16#
Given -
Curve is defined by the cubic function -
#y=x^3-2x#
Point#(2,4)# is on the curveWe have to know the slope of the curve at point
#(2,4)# Slope of the curve at any point on the curve is given by its first derivative.
#dy/dx=3x^2-2# At
#x=2# the slope is
#y=(3.(2^2)-2=12-2=10# The equation of the tangent -
#c+mx=y#
#c+10.2=4#
#c=4-20=-16# Then
#y=10x-16#
By signing up, you agree to our Terms of Service and Privacy Policy
To find the equation of the tangent line to the curve y=x^3 - 2x at the point (2,4), we need to find the slope of the tangent line at that point.
First, we find the derivative of the function y=x^3 - 2x. The derivative is given by dy/dx = 3x^2 - 2.
Next, we substitute x=2 into the derivative to find the slope at the point (2,4). So, dy/dx = 3(2)^2 - 2 = 10.
Therefore, the slope of the tangent line at the point (2,4) is 10.
Using the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we substitute the values (2,4) and m=10 into the equation.
Hence, the equation of the tangent line to the curve y=x^3 - 2x at the point (2,4) is y - 4 = 10(x - 2).
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.
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)=-5x+2# from [2,4]?
- What is the equation of the line tangent to # f(x)=x^2-sqrt(e^x-3x) # at # x=0#?
- Find all points where the tangent line is horizontal: #x^2+xy+y^2=1#?
- What is the equation of the normal line of #f(x)=2x^4+4x^3-2x^2-3x+3# at #x=-1#?
- How do you use the limit definition to find the derivative of #f(x)=1/(4x-3)#?

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