Answer:
m is 4 or -12.
Step-by-step explanation:
y = 2x^2 - 4x + 8.
To find the slope of the tangent at the point (x, y) we find the derivative.
y' = 4x - 4.
So m = 4x - 4.
Now our straight line is y = mx and m = 4x - 4 so
When y = mx meets the curve
mx = 2x^2 - 4x + 8
x(4x - 4) = 2x^2 - 4x + 8
4x^2 - 4x = 2x^2 - 4x + 8
2x^2 = 8
x^2 = 4
x = ±2.
So the line meets the curve and is tangent to it at the points where x = 2 and x = -2.
So the value of m 4(2) - 4 = 4
or 4(-2) - 4 = -12.
