anonymous
  • anonymous
Two hard calculus problems? Find the critical number of the function. g(t) = | 6t - 9 | t = Find the critical points of the function. F(x) = x^4/5(x - 7)^2 x = (smallest value) x = x = (largest value)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Critical point of the function, is point where a function obtains it's local maximium or mínimum value. You know how graph of g(t) = | 6t - 9 | looks like?
anonymous
  • anonymous
relative minimum of the graph of |6t - 9| is at (1.5, 0) and the derivative of g(t) at 1.5 is undefined (one-sided limits are different) Thus, critical number is t = 1.5 To find the critical numbers, find when f'(x) = 0 or is undefined f(x) = x^4/5(x - 7)^2 f'(x) = [4x^3(5(x - 7)^2 - 10(x-7)*x^4]/(25(x-7)^4) f"(x) = [20x^3(x - 7)^2 -10x^4(x - 7)]/(25(x-7)^4) which reduces by (x - 7) f'(x) = [20x^3(x - 7) -10x^4]/(25(x - 7)^3) setting the numerator = 0 and factoring 10x^3[2(x - 7) - x] = 0 10x^3 (x - 14) = 0 x = 0 , x = 14 are two critical numbers The denominator = 0 at x = 7 (undefined) 0, 7, 14
anonymous
  • anonymous
Thanks archie, amazing! :)

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