anonymous
  • anonymous
if f(x)= 4x^3-21x^2+36x-4, then the graph of f is decreasing and concave up on the interval...
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
would you like the choices?
anonymous
  • anonymous
a. (3/2, 2) b. (neg. infinity, 7/4) c. (7/4, infinity) d. (7/4, 2) e. (3/2, 7/4)
anonymous
  • anonymous
A plot is attached
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mathmate
  • mathmate
Given f(x)= 4x^3-21x^2+36x-4. The graph is decreasing when f'(x)<0. f'(x)=12x^2-42x+36 which factors into f'(x)=6(x-2)(2x-3). This means that f'(x) is negative (f(x) decreasing) between 1.5 and 2, or (1.5,2). For concavity, we look at f"(x)=24x-42=6(4x-7), which means that f(x) is concave up when x>7/4, or (7/4,+inf) Therefore f(x) is increasing and concave up between 7/4 and 2, or (7/4,2)
anonymous
  • anonymous
ah thank youu!!

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