Question
Show that the curve y=6x^3+5x-3 has no tangent line with slope 4.
The answer key says that
m=y'=18x^2+5, but x^2 is greater than or equal to 0 for all x, so m is greater than or equal to 5 for all x.
I don't understand that x^2 is greater than or equal to zero. Where did that come from? Why isn't x all real numbers?
The answer key says that
m=y'=18x^2+5, but x^2 is greater than or equal to 0 for all x, so m is greater than or equal to 5 for all x.
I don't understand that x^2 is greater than or equal to zero. Where did that come from? Why isn't x all real numbers?
Answers
y' = 18x^2 + 5
we want 18x^2 + 5 = 4
18x^2 = -1
x^2 = -1/18
but that is not possible since the square of anything has to be positive,
so there is value of x making this equations true
thus there is not slope of 4
thuse there is no such tangent
we want 18x^2 + 5 = 4
18x^2 = -1
x^2 = -1/18
but that is not possible since the square of anything has to be positive,
so there is value of x making this equations true
thus there is not slope of 4
thuse there is no such tangent