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fenix001 [56]
1 year ago
10

Find the critical numbers of the function. (enter your answers as a comma-separated list. if an answer does not exist, enter dne

. ) f(x) = x4/5(x − 8)2
Mathematics
1 answer:
NNADVOKAT [17]1 year ago
3 0

The critical values of the function are x = 0 and x = 64

The critical values of a function f(x) are the values of x for which f'(x) = 0.

Given,

f(x) = \frac{x^{4} }{5(x-8)^{2} }

The derivative is found as follows, applying the quotient rule:

f'(x) = \frac{[5(x^{4} )(x-8)^{2}-5x^{4} [(x-8)^{2} ]' }{[5(x-8)^{2} ]^{2}  }

     = \frac{2x^{3}(x-64) }{5(x-8)^{3} }

The zeros of the function are the zeros of the numerator, thus:

2x^{3} (x-64) =0\\2x^{3} =0-------- > x =0\\

x - 64 = 0------------->x = 64

The critical values are x = 0 and x = 64

Learn more about critical values here:brainly.com/question/12958088

#SPJ4

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