Consider the following.
Find the critical numbers. (Enter your answers as a commaseparated list. If an answer does not exist, enter DNE.)
Find the open intervals on which the function is increasing or decreasing. Use a graphing utility to verify your results. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
increasing 

decreasing 

f(x) = −5x^{2} + 40x
Hence, f'(x) = 10x + 40
The critical values of x are those values of x at which f'(x) is zero or it doesn't exist.
f'(x) = 10x + 40 = 0
Hence, x = 40/10 = 4
f'(x) exists at all the points and values of x as it's a polynomial function.
Hence, the crtical number is:
x = 4
If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I.
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