Calculus 1 Question

Question

Let f(x)={(7x-9x^2 for x<0), (6x^2+7x for x>=0)}

According to the definition of the derivative, to compute f'(0), we need to compute the left-hand limit

lim x->0- ____________ which is _____(7)

and the right-hand limit

lim x->0+ ____________ which is _____(7)

We conclude that f'(0)=_____(7)

*I found the derivatives of both parts of the function and determined that they are both equal to 7, and therefore f'(0)=7. This is correct, however I'm not sure what to put in the other blank spot next to "limx->0-/+". I've already tried putting the derivatives there but that doesn't work.*

Answer 1

Is this being down in some online system? Because it makes sense to me for you to do as you did. Place the derivatives in the first blank space, and then the result, which is 7.

Makes sure you're not mixing up the order here. For x -> 0+, you should put the derivative that applies for the function definition where "x>0".