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How many critical points does the function f(x) = (x+2)^5 (x-3)^4have?

User Asara
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Final answer:

The function f(x) = (x+2)^5 (x-3)^4 has two critical points, which are found by setting its derivative equal to zero and solving for x.

Step-by-step explanation:

The number of critical points of a function is found by taking the derivative of the function and setting it equal to zero to solve for values of x. The function in question is f(x) = (x+2)^5 (x-3)^4. To find the critical points, we differentiate the function:

f'(x) = 5(x+2)⁴(x-3)⁴ + 4(x+2)⁵(x-3)³

To find the critical points, we set the derivative equal to zero:

0 = f'(x) = 5(x+2)⁴(x-3)⁴ + 4(x+2)⁵(x-3)³

The x values that make this true are x = -2 and x = 3, as these would make a factor in the derivative equal to zero. This means the function f(x) has two critical points.

User Norbert Huurnink
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