Application of first derivative: Local Max/Min

1. Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.  solution

(a) \(f(x)=5x+2 \)     (b) \( f(x)=3-2x \)

2. Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.  solution

\(f(x)=5x^2+2x+3\)

3. Find the critical numbers of the function    \( f(x) =  x^3+x^2-x \)   solution

4. Consider \(f(x) = x^3 + 3x^2 - 9x + 10\). Answer the following using calculus.     solution

(a)  Find the intervals on which \( f \) is increasing or decreasing.

(b)  Find the \(x\)-values where \(f\) attains its local maximum and minimum values.

5. Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.  \(f(t)=\dfrac{t}{t-5}\)  solution

6. Find the local maximum and local minimum values of \(f(x)=x^2e^x \). solution