19. Write an equation to represent the relationship
1 answer:
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Well, is the function continuous? yes, is a cubic one, you can graph it if you wish, is continuous all the way, and of course at [ 0, 4] too.
is it differentiable? you can always look at the graph between 0,4 and is a smooth transition line, thus yes, it is differentiable, but let's check anyway,
its derivative has no asymptotes and therefore no "cusps", so yes, is differentiable all around.
is f(0) = f(4), let's check
f(0) = 0+0+0+3, f(0) = 3
f(4) = 64 - 16 - 48 + 3, f(4) = 3
yeap
there must then be a "c" value(s) with a horizontal tangent slope, let's check, is really just the critical points.
is it differentiable? you can always look at the graph between 0,4 and is a smooth transition line, thus yes, it is differentiable, but let's check anyway,
is f(0) = f(4), let's check
f(0) = 0+0+0+3, f(0) = 3
f(4) = 64 - 16 - 48 + 3, f(4) = 3
yeap
there must then be a "c" value(s) with a horizontal tangent slope, let's check, is really just the critical points.
Answer:
3(t+2)
Step-by-step explanation:
As with any problem involving division of fractions, you can invert the denominator and multiply.
Your knowledge of the factoring of the difference of squares helps. If that doesn't work for you, you can always use synthetic division or polynomial long division to find the quotient of (t^2-4) and (t-2).