5. Graphical Applications of Derivatives

Identify the open intervals on which the function is increasing or decreasing.

$f(x)=3x^4+8x^3-18x^2+7$

Identify the open intervals on which the function is increasing or decreasing.

$f(x)=x^{2/3}(4-x)$

Identify the intervals on which the function is increasing or decreasing.

$f(x)=\sin^2x$ on $[0,\pi]$

Identify the local minimum and maximum values of the given function, if any.

$f\left(\theta\right)=\sin\theta+\cos^2\theta$ on $[0,π]$

First Derivative Test

a. Locate the critical points of f.

b. Use the First Derivative Test to locate the local maximum and minimum values.

c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist).

f(x) = x² + 3 on [-3,2]

First Derivative Test

a. Locate the critical points of f.

b. Use the First Derivative Test to locate the local maximum and minimum values.

c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist).

f(x) = x√(4 - x²) on [-2,2]

First Derivative Test

a. Locate the critical points of f.

b. Use the First Derivative Test to locate the local maximum and minimum values.

c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist).

f(x) = 2x⁵ - 5x⁴ - 10x³ + 4 on [-2,4]

First Derivative Test

a. Locate the critical points of f.

b. Use the First Derivative Test to locate the local maximum and minimum values.

c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist).

f(x) = x²/(x² - 1) on [-4,4]