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Class 12 Mathematics Chapter 6 Applications Of Derivatives Quiz 8 (25 MCQs)

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1. Let y = x$^{3 }$Find the differential when x =2 and dx = 0.1.
2. If f "(x) >0, what is true about f(x)?Note:you are given the second derivative.
3. If a cone of maximum volume is inscribed in a given sphere, then the ratio of the height of the cone to the diameter of the sphere is
4. What values separate intervals of increasing and decreasing?
5. Projectiles on Earth follow parabolic trajectories. What would have to be true in order for projectiles to follow cubic trajectories?
6. Evaluate:$\int_0^3\left(x+1\right)^{\frac{1}{2}}dx$
7. If a function's FIRST derivative is negative at a certain point, what does that tell you?
8. A ladder is 10 meters long and is leaning against a wall. If the bottom of the ladder is sliding away from the wall at a rate of 2 m/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 meters from the wall?
9. We want to construct a box whose base length is 3 times the base width. If the box must have a volume of 50 ft$^{3}$, determine the dimensions that will minimize the amount of material used.
10. Differentiate (2x + 2)(x-5)$^{8}$ with respect to x.
11. Let $f\left(x\right)=x^4+ax^2+b, $ $x=1.$
12. A function is what if its second derivative is negative?
13. If (a, b) is a local minimum, then what will be true about f'(a)?
14. What is the equation of the line tangent to y= x$^{2}$+2x-1 at x=1?
15. F has critical numbers of-3, 0, and 1. If $f" (x) =-3x^2 + 4x$
16. Given:MR(x)=100-5x, MC(x)=20 + 2x. Solve MR = MC to find profit-maximizing output.
17. When a car's velocity is positive and its acceleration is positive, what is happening to the car's motion?
18. If f'(x) = 0 what does that imply about the x value?
19. When f'(x) changes from positive to negative, there is(are) .....
20. The derivative of the function g is $g'\left(x\right)=\cos\left(\sin x\right).$ $x=0$
21. A particle moves in a straight line with a velocity of v(t) = 2t$^{2}$. How far does the particle move between times t = 1 and t = 3?
22. For a function g(x), g'(-2)=0 indicates that x=-2 is .....
23. Identify the conclusion of the Mean Value Theorem.
24. S(t) = t$^{2}$-20 Find the average velocity from t = 3 to t = 5.
25. A farmer wants to construct a rectangular pigpen using 400 ft of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area? NO CALC
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