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n, they will drive from Fort Worth to San Antonio, a distance of 229 miles, to visit his grandparents. On the way back, Mike reverses his trip and travels from San Antonio to Dallas through Forth Worth. Write one equation to show the distance traveled from Dallas to San Antonio, and a second equation to show the distance traveled from San Antonio to Dallas. What do you notice about the distance traveled each w

Step-by-step explanation:

n, they will drive from Fort Worth to San Antonio, a distance of 229 miles, to visit his grandparents. On the way back, Mike reverses his trip and travels from San Antonio to Dallas through Forth Worth. Write one equation to show the distance traveled from Dallas to San Antonio, and a second equation to show the distance traveled from San Antonio to Dallas. What do you notice about the distance traveled each w

4 0

2 years ago

f(x) = x4 - 50x2 + 3 (a) Find the intervals on which f is increasing. (Enter the interval that contains smaller numbers first.)

shtirl [24]

Answer:

(-5, 0) ∪ (5, ∞)

Step-by-step explanation:

I find a graph convenient for this purpose. (See below)

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When you want to find where a function is increasing or decreasing, you want to look at the sign of the derivative. Here, the derivative is ...

f'(x) = 4x^3 -100x = 4x(x^2 -25) = 4x(x +5)(x -5)

This has zeros at x=-5, x=0, and x=5. The sign of the derivative will be positive when 0 or 2 factors have negative signs. The signs change at the zeros. So, the intervals of f' having a positive sign are (-5, 0) and (5, ∞).