Find the equation of the tangent at the point (2,4) to the curve y=x³-2x.

[Kitimbo]

Find the equation of the tangent at the point (2,4) to the curve y=x³-2x.

Find the equation of the tangent at the point (2,4) to the curve y=x³-2x.Also find the coordinates of the point where the tangent meets the curve again.

Help me with the second part

 

[Deleted member 4993]

Find the equation of the tangent at the point (2,4) to the curve y=x³-2x.Also find the coordinates of the point where the tangent meets the curve again.

Help me with the second part

Since you have done the first part - what was the equation of the tangent line?

 

[Kitimbo]

10x-y-16=0

 

[Deleted member 4993]

10x-y-16=0

y = 10*x - 16
Now replace 'y' in the first equation of the graph (y=x³-2x.), using the equation above, and solve for 'x's then 'y's.

 

[JeffM]

Find the equation of the tangent at the point (2,4) to the curve y=x³-2x.Also find the coordinates of the point where the tangent meets the curve again.

Help me with the second part

This gives the same result as your way, but is a different way to organize your thoughts. Put notation to work for you.

Let f(x) be the curve and g(x) be the line of tangency at (2, 4). Function notation was taught to you for a reason.

\(\displaystyle \therefore g(2) = f(2) = 4\ and\ g'(2) = f'(2).\)

\(\displaystyle f(x) = x^3 - 2x\ and\ g(x) = a + bx \implies f'(x) = 3x^2 - 2\ and\ g'(x) = b.\)

This just turn the words into function notation.

\(\displaystyle f'(2) = g'(2) = b \implies b = 3 * 2^2 - 2 = 10.\)

\(\displaystyle 4 = g(2) = a + 10(2) \implies a = -\ 16 \implies g(x) = 10x - 16.\) You got here on your own.

Now solve \(\displaystyle x^3 - 2x = 10x - 16\)

Hint for solving the cubic: x = 2 is one solution as you already know.

What is your final step?

 

[Kitimbo]

Am not arriving to the answer coz it must be one!!!

 

[mmm4444bot]

Am not arriving to the answer coz it must be one!!!

If you would like us to check your work, you will need to post it. :cool:

 

[Kitimbo]

Thanks I finally arrived to the answer.
Its (-4,-56).I solved the equation using polynomial division the after I got 3 values of x of which 2 where repetitive so I took -4 the I substituted it into equation of the curve to get the y value.

 

[JeffM]

Thanks I finally arrived to the answer.
Its (-4,-56).I solved the equation using polynomial division the after I got 3 values of x of which 2 where repetitive so I took -4 the I substituted it into equation of the curve to get the y value.

Well done.