Does the parabola y = 2x^2 - 13x + 5 have a tangent whose slope is -1. If so, then it will be?
Answer: y= -x-13
Explanation
To find the slope of the tangent to the parabola y = 2x^2 - 13x + 5, we need to find the derivative of y with respect to x.
dy/dx = 4x - 13
We want to find if there is a point where the slope of the tangent is -1.
4x - 13 = -1
4x = 12
x = 3
Now, we need to find the corresponding y-coordinate.
y = 2(3)^2 - 13(3) + 5
y = 18 - 39 + 5
y = -16
So, the point of tangency is (3, -16).
The equation of the tangent line is:
y - (-16) = -1(x - 3)
y + 16 = -x + 3
y = -x - 13
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