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

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1. If a function has a first derivative that is negative, what does that tell you?
2. It is a conditional concept that can be transformed into an equation which is a part of an optimization problem.
3. The population of a town x years after 2000 is modeled by P(x). What is the best interpretation of P'(10) = 50.
4. Find the second derivative of f(x) = x$^{2 }$+ e$^{x }$-cosx
5. How many critical numbers does f have if $f'\left(x\right)=(x-2)^2(x+5)$
6. If total cost C(x)=2x$^{2}$ + 10x + 50, find MC(x).
7. What is a point of inflection?
8. What is the maximum value of f(x) = x$^{3}$-3x$^{2}$-1 on the interval [-3, 2]?$_{}$
9. For what value of c is the Rolle's thm applicable on the given function f(x) = x$^{2}$-5x+4 [1, 4]
10. The point on the curve $y^2=4x$
11. A triangular trough is 10 ft long, 6 ft wide across the top, and 3 ft deep. If water flows in the rate of 12 ft/min, find how fast the surface is rising when the water is 6 inches deep?
12. F(x) increases when .....
13. Find the derivative of f(x) = x$^{2}$sinx
14. If $f\left(x\right)=\sin\left(\frac{x}{2}\right), $ $c$ $\frac{\pi}{2}
15. What's the difference between Rolle's Theorem and the Mean Value Theorem?
16. For a function g(x), g" (3)=-8 indicates that g(x) is ..... at x=3.
17. Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the angle between the tip of the ladder and the house changing when the ladder is 5 ft high? Hint:Use a trig function.
18. Find the fourth derivative of the following functions with respect to x. $y=3x^2+5x-1$
19. A light is placed on the ground 30 ft from a building. A man 6 ft tall walks from the light toward the building at the rate of 5 ft/sec. Find the rate at which the length of his shadow is changing when he is 15 ft from the building.
20. Which of the following is the absolute maximum value of the function y = x$^{3}$-3x$^{2}$-1 on the given interval [-1, 4]?
21. A function is what if its second derivative is positive?
22. If the total cost function of producing x units of a commodity is given by $360-12x+2x^2$
23. What is a vertical tangent?
24. When f'(x) changes from positive to negative at a Critical Value, then there is .....
25. Which of the following is the absolute minimum point of the function y = x$^{3}$+ 6x$^{2}$-12 on the given interval [-2, 5]?
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