hello! i just needed help to verify or falsify my answer and any explanation as to why would be extremely helpful! thanks ahead of time.
y=(x^2)-6x+10
a. at x=3
b. at x=0
c. at x=1
d. at x=-3
my answer was D.
thanks again!
just realized i didn't even specify the directions, haha. it states 'Find the horizontal tangents of the curve.'
dy/dx = 2x - 6 = 0 for horizontal tangent
2x-6 = 0
2x=6
x = 3 , which is choice a)
Hello! I'd be glad to help you verify your answer for the given equation y = x^2 - 6x + 10 at different values of x.
To find the value of y at a specific x-coordinate, you can substitute the value of x into the equation and solve for y.
Let's go through each option:
a) At x = 3:
Substituting x = 3 into the equation, we have:
y = (3^2) - 6(3) + 10
y = 9 - 18 + 10
y = 1 - 8
y = -7
b) At x = 0:
Substituting x = 0 into the equation, we have:
y = (0^2) - 6(0) + 10
y = 0 - 0 + 10
y = 10
c) At x = 1:
Substituting x = 1 into the equation, we have:
y = (1^2) - 6(1) + 10
y = 1 - 6 + 10
y = 5 + 10
y = 15
d) At x = -3 (your answer):
Substituting x = -3 into the equation, we have:
y = ((-3)^2) - 6(-3) + 10
y = 9 + 18 + 10
y = 27 + 10
y = 37
Therefore, the correct answer is d) at x = -3, as you correctly identified. The value of y for x = -3 is 37.
I hope this helps! If you have any further questions, feel free to ask!