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Chapter 2: Problem 10

Find the key numbers of the expression. $$9 x^{3}-25 x^{2}$$

Short Answer

Expert verified
The key numbers of the function are x=0 and x=50/27.

Step by step solution

01

Differentiate the given function

Start by finding the derivative of the function. Using the power rule for differentiation which states that the derivative of \(x^n\) is \(n*x^{n-1}\), then the derivative of the given function is: \(f'(x) = 27x^2 - 50x\) .
02

Set the derivative to zero

Next, set the derivative equal to zero to find the x-values, where the original function might have maximum or minimum values: \(27x^2 - 50x = 0\).
03

Solve for x

Factor out the common factor, which in this case is x, yielding: \(x(27x - 50) = 0\). Then solve for x. This equation is true when x=0 and x=50/27.

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