+318 Let f(x)= x^3+3x^2-24x+23
** I ALREADY GOT THE FIRST PART. IT SAYS USE DEFINITION OF A DERIVATIVE to find f'(x)= 3x^2+6x-24
please help with these::::
b) use the definition of a derivative to find f '' (x)= _____??
c) on what interval is f increasing (include the endpoints in the interval)=___???
d) interval f decreasing =_____???
e) what interval is f concave downward???____?
f) interval is f convave upard???____
+9519 You can use the definition of derivative on \(f'(x)\) to find \(f''(x)\) because \(f''(x) = \displaystyle\lim_{h\to0}\dfrac{f'(x + h) - f'(x)}{h}\).
If f is increasing on an interval \(\mathcal I\), then for all real numbers \(x\in \mathcal I\), \(f'(x) \geqslant 0\).
If f is decreasing on an interval \(\mathcal I\), then for all real numbers \(x\in \mathcal I\), \(f'(x) \leqslant 0\).
If f is concave downward on an interval \(\mathcal I\), then for all real numbers \(x\in \mathcal I\), \(f''(x) \leqslant 0\).
If f is concave upward on an interval \(\mathcal I\), then for all real numbers \(x\in \mathcal I\), \(f''(x) \geqslant 0\).
These are the definitions. I believe you can finish the rest with these.
