# Math 1251 Practice T-F questions

1. The equation of the tangent line to the curve y=f(x) at the point (a,f(a)) is y-f(a)=f'(x)(x-a).

2. The derivative with respect to x of f(x)/g(x) is f'(x)/g'(x).

3. If f(0)=0, then f'(0)=0.

4. If f(x) is differentiable at x=2, then f(x) is continuous at x=2.

5. If f(x) approaches infinity as x approaches 0, then x*f(x) also approaches infinity as x approaches 0.

6. If lim_{x->2} f(x)=4, and lim_{x->3} g(x)=7, then lim_{x->5} (f(x)+g(x))=11.

7. The derivative with respect to x of \pi^6 is 6*\pi^5.

8. If f(x)->infinity, g(x)->infinity as x->infinity, then f(x)/g(x) could either ->infinity, ->0, or go to any constant as x->infinity.

9. There is no function which grows more rapidly than f(x)=e^x as x->infty.

10. If f(x) has a local minimum at x=2, then f'(2)=0.

11. If f''(x) exists and is >0 for all x, then f(x) is an increasing function of x.

12. The derivative with respect to x of x^x is x*x^{x-1}.

13. If f(1)=2, and f(3)=-3, and f(x) is continuous on [1,3], then f(a)=0 for some a in (1,3).

14. If f'(x)->0 as x->infinity, then we must also have f(x)-> a constant c as x->infinity.

15. If f(x) has a local minimum on the interval (1,2), then the absolute minimum of f(x) on [1,2] cannot occur at x=1.

16. If f(5)=2, f(7)=9, then f'(6)=7/2.

17. The best linear approximation to e^(2x) at x=0 is 1+2x.

18. If f(x) is differentiable at x=2, and f(x) has a local maximum at x=2, then f'(2)=0.

19. If f(x) is continuous on [2,4], then f(x) must have an absolute maximum on [2,4].

20. If f(x) and g(x) both have local maxima at x=2, then f(x)*g(x) also has a local maximum at x=2.

21. The 12th derivative with respect to x of any polynomial in x of degree 10 is 0.

22. If f(x)=f'(x) for all x, then we also have that f''(x)=f(x) for all x.

23. The function y=log(x) is increasing and concave downward for x>0.

24. If f'(0) does not exist, then lim_{x->0} f(x) does not exist.

25. The nth derivative of e^(x) is e^x.

26. The function f(x)=2-x^2 on the real line is a 1-1 function.

27. For any cubic polynomial p(x) with real coefficients there is a real number x such that p(x)=0.

28. If f(x) approaches 0 when x-> \infinity, then we must also have that f'(x) approaches 0 as x-> \infinity.

29. If f''(0)=0, then x=0 must be a point of inflection of the graph y=f(x).

30. If f(x) is a 1-1 function with domain the real numbers, then f'(0) cannot be equal to 0.

31. If p(x) is a polynomial in x, then p'(x) is a polynomial in x.

32. If f(x) is continuous on the interval [1,3], f(x)>=0, f(2)=0, then f has a local minima at x=2.

33. The nth derivative of ln(x) is 1/x^n.

34. If p(x) is a polynomial with p(2)=5=p(3), then there is some number c, 2 35. There is some function f(x) such that f(x)>0, f'(x)<0, f''(x)>0 for all x.