Question

determine whether the curve has a tangent at the indicated point. if it does, give its slope, if not explain why not

F(X)= { 2-2x-x^2, x<0
2x + 2 x>=0 at x = 0

Answer 1

To tell if a function is continuous at a specific point, the limit from the left and right must be equal, in this case that would mean
2x + 2 = 2 -2x - x^2 when x =0

Answer 2

my question is how can u even have a point if

Answer 3

a point at x = 0 if the domain restriction is x>0

Answer 4

and y do the slopes have to be equal ye i know all the formulas i want to know y so if it is conceptual problem or another problem that requires me to do this ( set the slopes equal) without telling me i need to do it, then i want to be able to do it

Answer 5

The idea is that the two different lines have to meet up at that point x=0 for the function to be continuous and differentiable at that point, that's all.

Answer 6

but how can u have a value if the domain says x>0

Answer 7

x<0*

Answer 8

Because F(x) is split up into two different equations.

Answer 9

ye and?