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Class 12 Mathematics Chapter 6 Applications Of Derivatives Quiz 4 (25 MCQs)

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1. $\lim_{h\rightarrow0}\left(\frac{5\left(x+h\right)^2-5x^2}{h}\right)$
2. The line $y=mx+1$ $y^2=4x$
3. How many points of inflection does a parabola have?
4. The Mean Value Theorem applies to f(x) = 3x-x$^{2}$ on the interval [2, 5]. Find the value of x where the slope of the tangent line is equal to the slope of the secant line
5. What is marginal cost?
6. If the position of a particle is represented by s(t) =-t$^{2}$ + 1, what is its position at t = 1?
7. Find the slope of the normal line at x = 9 of $f\left(x\right)=\sqrt{x}$
8. Find the critical points of f(x) = 2x$^{4}$-4x$^{2}$ + 1
9. The value of c guaranteed to exist by the MVT for $f\left(x\right)=x^2$
10. A railroad track and a road cross at right angles. An observer stands on the road 70 meters south of the crossing and watches an eastbound train traveling at 60 meters per second. At how many meters per second is the train moving away from the observer 4 seconds after it passes through the intersection?
11. If h = f(a) gives height h (in inches) of a child aged a years, then dh/da is positive when 0 < a < 10.
12. The linearization of function y=f(x) near the value x=a is given by:
13. When does Newton's method fail to find an approximate zero of a function?
14. If a function has a derivative that is positive, what does that tell you?
15. A function f(x) has derivative f'(x) = 3x-6. On which interval is f increasing?
16. Given that $f\left(x\right)=2x^4-3x^3+4x^2$ $f^{" '}\left(x\right)$
17. If a function has a second derivative that is negative, what does that tell you?
18. Find the derivative of the given equationf(x) = 1/x$^{2 }$(hint:use your pink sheet)
19. The tangent line to f(x)$^{}$=x$^{3}$+kx$^{2}$ at x = 1 is parallel to the line containing points (2, 9) and (3, 10). What is the value of k?
20. Which of the following describes an interval of f(x) that is both decreasing and concave up?
21. To be called a point of inflection of a function, what must what happen?
22. Let f(x) = x$^{3 }$and L(x) be the linearization of f(x) centered at x = 2. Find L(x).
23. If MR(x) > MC(x) at output x, the profit-maximizing rule suggests:
24. A man 6 ft tall walks away from a lamp post 16 ft high at the rate of 5 miles per hour. How fast does the shadow lengthen?
25. The minimum value of $\frac{x}{\log_ex}$
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