- #1
naaa00
- 91
- 0
Hello people!
Well, I am doing some excercises for fun. Picked some Precalculus stuff, and found this excercise: "Construct a function that has the same slope at x = 1 and x = 2. Then find two points where y = x^4 - 2x^2 has the same tangent line (draw the graph)." I have found a solution, but I think the solution is totally wrong. Any advice?
What I did:
For the first part made up y = x^3 + 1
Then, I plotted two points: (1,2) (2,9) where (a,f(a)) and (b,f(b)).
Calculated the slope and got 7.
two-point form: y - 2=7(x - 1)
y = 7x - 9 slope-form. Secant line.
y= 7 Tangent line.
For the second par did something similar:
I plotted points: (2,24) (3,81) for y = x^4 - 2x^2
The slope is 57.
Thw two-point form: y -24 =57(x - 2)
y = 57x - 90 slope-form. Secant line.
y = 57 Tangent line.
It must be wrong, but I can not say why.
Also tried the following:
Since two points have the same tangent line, or derivative, f'(a) = f'(b)
And y = x^4 - 2x^2
when x = a
y = a^4 -2a^2 and y = b^2 - 2b^2
Then: f'(a) = f(a) - f(b)/ a - b
f'(b) = f(b) - f(a)/ b - a
End up needing to solve for two equations, but everything gets to messy, and surely must be wrong.
I think I am confused.
Any correction?
Thanks in advanced!
Well, I am doing some excercises for fun. Picked some Precalculus stuff, and found this excercise: "Construct a function that has the same slope at x = 1 and x = 2. Then find two points where y = x^4 - 2x^2 has the same tangent line (draw the graph)." I have found a solution, but I think the solution is totally wrong. Any advice?
What I did:
For the first part made up y = x^3 + 1
Then, I plotted two points: (1,2) (2,9) where (a,f(a)) and (b,f(b)).
Calculated the slope and got 7.
two-point form: y - 2=7(x - 1)
y = 7x - 9 slope-form. Secant line.
y= 7 Tangent line.
For the second par did something similar:
I plotted points: (2,24) (3,81) for y = x^4 - 2x^2
The slope is 57.
Thw two-point form: y -24 =57(x - 2)
y = 57x - 90 slope-form. Secant line.
y = 57 Tangent line.
It must be wrong, but I can not say why.
Also tried the following:
Since two points have the same tangent line, or derivative, f'(a) = f'(b)
And y = x^4 - 2x^2
when x = a
y = a^4 -2a^2 and y = b^2 - 2b^2
Then: f'(a) = f(a) - f(b)/ a - b
f'(b) = f(b) - f(a)/ b - a
End up needing to solve for two equations, but everything gets to messy, and surely must be wrong.
I think I am confused.
Any correction?
Thanks in advanced!
Last edited: