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Class 12 Mathematics Chapter 6 Applications Of Derivatives Quiz 3 (25 MCQs)

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1. What are identified by finding where the second derivative equals zero or is undefined?
2. If f"(x) >0, what is true about f(x)?
3. Given a function g(x), if g'(x)=0 at a certain value of x, then g(x) has ..... at x.
4. If R(w) = w$^{3}$ then R'(-2) is negative.
5. If demand becomes more elastic after a price change, a firm is more likely to:
6. If f(x) = $3x^2 + 12x-4$
7. It is a part of the problem that needs to be maximized or minimized.
8. If a function is concave down at a critical number, what must occur at that critical number?
9. A conical tank is being filled with water at a rate of 3 cubic meters per minute. If the tank has a height of 10 meters and a radius of 5 meters, how fast is the water level rising when the water is 6 meters deep?
10. If $y=x^x, $ $\frac{dy}{dx}$
11. The concavity of a function is described by its .....
12. How many possible points of inflection does f have if $f'\left(x\right)=(x-2)^2(x+5)$
13. The function f is twice differentiable with f(2) = 1, f'(2)=4, and f" (2)=3. What is the value of the approximation of f(1.9) using the line tangent to the graph of f at x = 2?
14. If the graphs of the marginal cost and marginal revenuefunctions C'(q) and R'(q) cross at q*, then marginal revenue is equal to marginal cost at q*.
15. Given a function, f(x), if f'(x)>0 over a certain interval, then f(x) is ..... over that interval.
16. A ladder 10 ft long is leaning against a wall. If the bottom of the ladder is pulled away from the wall at a rate of 2 ft/s, how fast is the top of the ladder sliding down the wall when the bottom is 6 ft from the wall?
17. . What is the nature of function f(x) = 7x-4 on R?
18. Find the given integral:$\int_{ }^{ }\cos\left(2x+3\right)dx$
19. Find $\frac{dy}{dx}$ $y^2=10x$
20. Find the point(s) of inflection for f(x) = 2(x)$^{1/5}$ + 3
21. What is the slope of the line tangent to the graph of y=ln(2x) at the point where x=4?
22. If you are looking at a sign chart, how do you find an inflection point?
23. Find the smallest perimeter for a rectangle with an area of 256 in$^{2}$.
24. What is a horizontal tangent?
25. How many points of inflection does the function $y=\frac{x+1}{x}$
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