f(x) =(x - 2)/(x - 1) satisfies the hypotheses of the Mean value Theorem (MVT) on the interval [-3, 0]. If it does, find all possible values of c satisfying the conclusion of the MVT.
2.How many real roots does the equation x^5 + 2x + 5 = 0 have?
3. If f is differentiable on (-2, 2) and f'(x) >=4 , -2 < x < 2 , find the largest value of M so that the in equality f(1) >= M holds for all f such that f(-1) = 7.
4.Sarah is driving her car very smoothly from A to D one day. At 6:00 pm she is travelling at 20 mph, while 25 minutes later she is travelling at 40 mph.
Calculus tells us that at some time between 6:00 pm and and 6:25 pm her acceleration is exactly x mph/h. Determine x.
5. Let f be the function defined by f(x) = 3 + 2x^1/3 .
Consider the following properties:
A. derivative exists for all x^6= 0 ;
B. has horizontal tangent at x = 0 ;
C. concave up on (0, infinity) .
Which property(-ies) does f have?
更新1:
Correction 改正: no.5 : A. derivative exists for x does not equal 6
