Analyze the graph of the function

The graph of f is shown below. For which value of x is minimum?​​

Identify the open intervals where the function is increasing or decreasing.​

Find the indefinite integral.​

The graph of f is shown below. For which values of x is zero?​

A double-slit apparatus with 6 × 10-5 m separation between the slits is illuminated with 490 nm coherent light. A viewing screen is located 2.1 m from the slits. Only Consider fringes on one side of the central maximum. What is the linear distance between the first dark fringe and the second dark fringe (measured in mm)? 

A person has a far point of 200 cm. The distance from the cornea-lens to the retina is 1.8 cm. Suppose the eye’s power of accommodation is 3 diopters. What is the refractive power of eyeglasses should be used so the person can see objects as close as 20 cm clearly? Ignore the gap between the eyeglasses and eyes.

Determine whether Rolle’s Theorem can be applied to the function on the closed interval . If Rolle’s Theorem can be applied, find all values of c in the open interval such that .​

Find the value of the derivative (if it exists) of the function  at the extremum point  .​

Consider an experiment using a diffraction grating with 3000 lines/cm, a screen 2.5 m away, and a 440-nm wavelength beam of light. How many bright fringes will be observed on one side of the central maximum? Noe that the answer is an integer.