Home > Calculus > Slope of a Curve at a Point

The curve Y= X^3-3x has a slope 3 at two points. Find the two points?

Answer 1

x = # \pmsqrt(2)#

We need to differentiate the equation of the line to find the gradient function:

#dy/dx = 3x^2 - 3#

We want to find the point at which the slope is a certain value, so we set the gradient function equal to the slope and solve the equation:

#\text{let } dy/dx = 3: 3 = 3x^2 -3#

Now we can solve this to find the x-coordinates. Then we substitute this into the equation of the line to find the y values.

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

Answer 2

Luke Alvarez

#(sqrt2,-sqrt2)" and "(-sqrt2,sqrt2)#

#"note that the slope is given by "dy/dx#

#dy/dx=3x^2-3=3#

#"solve "3x^2-6=0#

#3x^2=6rArrx=+-sqrt2#

#"substitute these values into y"#

#x=sqrt2toy=(sqrt2)^3-3sqrt2=2sqrt2-3sqrt2=-sqrt2#

#x=-sqrt2toy=(-sqrt2)^3+3sqrt2=sqrt2#

#"the 2 points are "(sqrt2,-sqrt2)" and "(-sqrt2,sqrt2)#

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

Answer from HIX Tutor

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.