evaluate this using three-step rule:
f(x) = x³-9
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evaluate this using three-step rule:f(x) = x³-9
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Answer:
To evaluate the derivative of the function f(x) = x³ - 9 using the three-step rule, we need to follow these three steps:
Step 1: Compute the derivative of the function.
Step 2: Substitute the given value of x into the derivative obtained in step 1.
Step 3: Simplify the expression obtained in step 2.
Step 1: Compute the derivative of the function.
The derivative of x³ is 3x², and the derivative of a constant is zero. Therefore, the derivative of f(x) = x³ - 9 is:
f'(x) = 3x²
Step 2: Substitute the given value of x into the derivative obtained in step 1.
Let's say we want to evaluate f'(2). We substitute x = 2 into f'(x) to get:
f'(2) = 3(2)²
f'(2) = 12
Step 3: Simplify the expression obtained in step 2.
We have evaluated the derivative of the function f(x) = x³ - 9 at x = 2 using the three-step rule. The final result is f'(2) = 12.