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11 questions
Suppose that for a twice differentiable function f (x), f '(x) > 0 and f ''(x) > 0 on the interval (1,3). If we use a linear approximation at x = 2 to estimate f (1.9), will that estimate be an underestimate or overestimate, and why?
Underestimate since f '' > 0 on (1, 3)
Overestimate since f '' > 0 on (1,3)
Underestimate since f ' > 0 on (1, 3)
Overestimate since f ' > 0 on (1, 3)
Suppose that the sides of a square increase from 3 cm to 3.3 cm. Estimate the change in the area of the square.
1.8 cm^{2}
1.89 cm^{2}
0.9 cm^{2}
19.8 cm^{2}
Using the tangent line approximation for
$f\left(x\right)=\sqrt{x}$ at x = 9, approximate $\sqrt{8.2}$ .3.133
2.867
2.863
2.733
2.712
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