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WB3.1 - MVT & EVT

Last updated over 5 years ago

8 questions

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Question 1

1.

A car is traveling on a straight road as shown in the piecewise linear function. Apply the MVT on this graph over the interval [8,20].

Question 2

2.

Let f be the function given by f(x)=x^{3}-3x^2. That are all values of c that satisfy the conclusion of the MVT of differential calculus on the closed interval [0,3]?

Question 3

3.

Find the extreme value(s) of f(x)=\frac{1}{\sqrt{4-x^2}} on the interval (-2,2).

Question 4

4.

If f is continuous for a \leq x \leq b and differentiable for a < x < b, which of the following could be false? Explain with evidence.

a) f'(c)=\frac{f(b)-f(a)}{b-a} for some c such that a < x < b
b) f'(c)=0 for some c such that a < c < b
c) f has a minimum value on a \leq x \leq b
d) f has a maximum value on a \leq x \leq b

Question 5

5.

Apply mean value theorem on h(t)=\frac{-t^2+1}{3t} over [-3,-1].

Question 6

6.

Apply MVT on g(t)=\left( 2t-2 \right)^{\frac{2}{3}} over [-4,1].

Question 7

7.

Find the absolute min and max of f(x)=-x^{3}-2x^2-x-1 over [-1,1].

Question 8

8.

Find the absolute min and max of w(x)=-\cos(x) over [-\frac{\pi}{6}, \frac{\pi}{4}].