**Question:**

If $f^{\prime}(x)$ changes its sign from positive to negative as $x$ increases through $c$ in the interval $(c-h, c+h)$, then $x=c$ is a point of____________

**Solution:**

First derivative test states that if *f *'(*x*) changes sign from positive to negative as *x* increases through *c*, then *c* is a point of local maxima, and *f*(*c*) is local maximum value.

Thus, if $f^{\prime}(x)$ changes its sign from positive to negative as $x$ increases through $c$ in the interval $(c-h, c+h)$, then $x=c$ is a point of local maximum.

If $f^{\prime}(x)$ changes its sign from positive to negative as $x$ increases through $c$ in the interval $(c-h, c+h)$, then $x=c$ is a point of ____local maximum_____.