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18.02.2020 •
Mathematics
The line tangent to the graph of g(x) = x^{3}-4x+1 at the point (2, 1) is given by the formula
L(x) = 8(x - 2) + 1.
Which of the following statements are true? Select all that apply.
A. The functions are approximately equal on the interval 1.9 smaller than or equal to x larger than or equal to 2.1.
B. The functions have the same y-intercept.
C. The slope of the line equals g'(0).
D. The functions are approximately equal on the interval 0.5 smaller than or equal to x larger than or equal 1.0.
E. The graphs intersect at the point (2,1).
F. The slope of the line equals g'(2).
G. None of the above are true.
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Ответ:
Using function concepts, it is found that the correct options are:
A. The functions are approximately equal on the interval 1.9 smaller than or equal to x larger than or equal to 2.1.E. The graphs intersect at the point (2,1). F. The slope of the line equals g'(2).-------------------------------------------
The value of x we are interested is x = 2, thus, considering a margin, the functions are approximately equal between x = 1.9 and x = 2.1, which means that option A is correct, while option D is not.The y-intercept of g isA similar problem is given at link
Ответ:
well, about A and D, I just plugged the values on the slope formula of
for A the values are 8.01 and 8.0, so indeed those "slopes" are close.![\textit{\huge \checkmark}](/tpl/images/0513/7366/b929d.png)
for D the values are -2.25 and 8.0, so no dice on that one.
for B, let's check the y-intercept for g(x), by setting x = 0, we end up g(0) = 0³-4(0)+1, which gives us g(0) = 1.
checking L(x) y-intercept, well, L(x) is in slope-intercept form, thus the +1 sticking out on the far right is the y-intercept, so, dice.![\textit{\huge \checkmark}](/tpl/images/0513/7366/b929d.png)
for C, well, the slope if L(x) is 8, since it's in slope-intercept form, the derivative of g(x) is g'(x) = 3x² - 4, and thus g'(0) = -4, so no dice.
for E, do they intercept at (2,1)? well, come on now, L(x) is a tangent line to g(x), so that's a must for a tangent.![\textit{\huge \checkmark}](/tpl/images/0513/7366/b929d.png)
for F, we know the slope of the line L(x) is 8, is g'(2) = 8? let's check
recall that g'(x) = 3x² - 4, so g'(2) = 3(2)² - 4, meaning g'(2) = 8, so, dice.![\textit{\huge \checkmark}](/tpl/images/0513/7366/b929d.png)
Ответ:
about $64
Step-by-step explanation:
4 x $15.99 = $63.96
round $63.96 to get $64