## 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