Finding where a function is increasing and decreasing. The figure below shows th

Question

Finding where a function is increasing and decreasing. The figure below shows the derivative of f' of f. Where is f increasing and where is f decreasing? What are the x-coordinates of the local maxima and minima of f? Finding where a function is increasing and decreasing. The figure below shows the derivative f of f where is f increasing and where is f decreasing? what are the x-coordinates of the local maxima and minima of f ? f' (x) 10 5/ 15 20 30 Part 1 Your answer is partially correct. Try again. f (x) is increasing for o 15

Explanation / Answer

Note: f is increasing when f ' > 0 and decreasing when f ' < 0. when f ' = 0 , the tangent is horizontal.

f ' < 0 for 0<x<10 and 25<x<30. Hence f(x) is decreasing for 0<x<10 and 25<x<30

f ' > 0 for 10<x<25. Hence f(x) is increasing for 10<x<25.

Local minima is x=a if f '(a)=0 and the function increases(f ' >0) at x>a and decreases (f ' <0) at x<a.
Hence, local minima is x= 10

Local maxima is x=b if f '(b)=0 and the function increases(f ' >0) at x<b and decreases (f ' <0) at x>b.
Hence, local maxima is x= 25

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