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Class 12 Mathematics Chapter 6 Applications Of Derivatives Quiz 7 (25 MCQs)

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1. A particle has positive velocity if it's position graph is
2. What is the linearization function L(x) for y = (2x-1)$^{2 }$for values of x near 3?
3. Find dy/dxxy+y$^{2}$=2
4. Let L(x) = 3(x-4)-2. Find L(3.9).
5. Find the derivative of the function:$g\left(t\right)=\tan\left(\cos4t\right)$
6. Evaluate the limit. $\lim_{x\rightarrow2}\\frac{x^2-4x+4}{x^3-12x+16}$
7. Marginal profit is equal to:
8. For a function f(x), f" (4)=0 indicates that x=4 is .....
9. Which if the following is not a correct notation for 'derivative?'
10. Find dy for the function y = 4x$^{2 }$+ x + 3.
11. If a function is concave up at a critical number, what must occur at that critical number?
12. Where does the function, f(x) = 2x$^{3}$-9x$^{2 }$+ 12x-3 have relative max/min values?
13. If $f'\left(x\right)=\frac{1}{1+x^2}$ $g'\left(x\right)=\frac{1}{\left(1+\frac{x^2}{4}\right)}\cdot\frac{1}{2}$ $x, $ $\lim_{x\rightarrow0}f\left(x\right)=\lim_{x\rightarrow0}g\left(x\right)=0, $ $\lim_{x\rightarrow0}\\frac{f\left(x\right)}{g\left(x\right)}=$
14. A kite is 40 ft high with 50 ft cord out. If the kite moves horizontally at 5 miles per hour directly away from the boy flying it, how fast is the cord being paid out?
15. What is the lowest point on a function called?
16. Find the given integral:$\int_{ }^{ }\left(x^3-3x\right)dx$
17. What is the equation of the normal line at x =-3 of $y=x^2+12x+11$
18. Water is flowing into a spherical tank with 6 foot radius at the constant rate of $30\pi$ $V=\frac{\pi h^2}{3}\left(18-h\right).$
19. A function is increasing if its first derivative is what?
20. What will be true at an inflection point?
21. Is your approximation in #14 an under or over approximation?
22. If (a, b) is a local MAXIMUM on f (x), then what will be true about f '' (a)?
23. For times t > 0, a particle moves on the x axis with its acceleration defined by a(t) = 6t-2. If the velocity of the particle is-7 at t = 1, then at what time is the particle at rest?
24. Derive y=e$^{3x}$
25. These are word problems that deal with the application of maximum and minimum value of a function.
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