# 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#

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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).

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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.

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