Question

Find the intervals where the given function is increasing and the intervals where it is decreasing
f(x)=-(x+2)^2-3

Answer 1

This is a kind of meaty problem. Steps: Find the derivative, set up an inequality f'(x)>0. Solve the inequality. The solution of the inequality will tell you where (what parts of the domain) the function is increasing (derivative greater than zero). The complement of that solution will give the decreasing parts.

Answer 2

Vertex is at (-2, -3)

parabola is concave down

LHS of the vertex has a positive gradient , RHS negative gradient



x < -2 increasing x > -2 decreasing