Using Derivatives to Graph Function

Let f be the function with derivative given by f'(x) = sin(x² + 1).  How many relative extrema does f have on the interval 2 < x < 4?

• Two
• Three
• Four
• Five

Let f be the function with derivative given by f'(x) = x² - 2/x.  On which of the following intervals is f decreasing?  (No Calculator)

• (-∞, 0]
• (-1, 0]
• (0, ∛2]
• (∛2, ∞)

Given a function, f(x), if f'(x)<0 over a certain interval, then f(x) is ____________ over that interval.

• decreasing
• increasing
• concave up
• concave down

Given a function, f(x), if f'(x)>0 over a certain interval, then f(x) is __________ over that interval.

• increasing
• decreasing
• concave up
• concave down

Given a function g(x), if g'(x)=0 at a certain value of x, then g(x) has _____________ at x.

• an inflection point
• a critical point
• a minimum
• a maximum

For a function g(x), g'(-2)=0 indicates that x=-2 is ________________.

• an inflection point
• a critical point
• a relative maximum
• a relative minimum

For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.

• increasing
• decreasing
• concave up
• concave down

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

Find the critical points of f(x) = 2x⁴- 4x² + 1

• x= 0
• x = -1, 1
• x = -1, 0, 1
• no critical points

What are the intervals of the graph increasing for f(x) = 2x⁴- 4x² + 1

• (-1,0)
• (0,1)
• (-∞,-1) and (1,∞)
• (0,1) and (-1,0)