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Class 12 Mathematics Chapter 6 Applications Of Derivatives Quiz 5 (25 MCQs)

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1. The velocity of an object is given as v = 2t + 3t$^{3}$. What is the acceleration of the object at t = 2 secs?
2. What is the "top of a hill" on a function (even if it is a cusp) called?
3. When f'(x) changes from positive to negative, there is .....
4. Evaluate:$\int_1^2x^{-3}dx$
5. Suppose that the sides of a square increase from 3 cm to 3.3 cm. Estimate the change in the area of the square.
6. If $x^y=e^{\left(x-y\right)}$ $\frac{dy}{dx}$
7. Find the differential dy of the function y = 4x$^{2}$+x+3
8. A 5 ft ladder is leaning against a wall and sliding towards the floor. The top of the ladder is sliding down the wall at a rate of 2 ft/sec. How fast is the base of the ladder sliding away from the wall when the base of the ladder is 3 ft from the wall?
9. A function is decreasing if its first derivative is what?
10. If the position function for a particle is s(t) =-t$^{2}$-t, what is the instantaneous velocity function for the particle?
11. What will be true at an inflection point? (select the best answer)
12. The absolute minimum value of x$^{4}$-x$^{2}$-2x+ 5
13. Find dy for 2xy$^{2}$$^{ }$-x$^{2}$ +$^{ }$y = 5 if x = 0 and dx = 0.01.
14. Find $\lim_{x\rightarrow0}\frac{\sqrt{1+x}-1}{\text{x}}$
15. Find the derivative of the function:$f\left(x\right)=e^x\sin x$
16. What is the equation of the line tangent to f(x)= 4x$^{2}$+2x-1 at x=0?
17. If the cost C (in dollars) of feeding x students in the dining center is given by C = f(x), then the units of dC/dx are dollars per student.
18. If f'(x) >0, then the function is
19. If a function has a second derivative that is positive, what does that tell you?
20. The position of an object is given as a function of time by x = 3t$^{2}$ + 5t$^{3 }$-2tWhat is the acceleration of the object at time t = 2 s?
21. If the line y = x touches the curve y = x$^{2}$ + bx + c at a point (1, 1) then
22. Let f(x) = x$^{3 }$and L(x) be the linearization of f(x) centered at x = 2. Calculate the approximation for f(2.1).
23. What is the equation of the line normal to f(x)=5x$^{5}$-2x at x =-1?
24. Let f(x) = $x^{(2/5)}$
25. What is the absolute maximum value of the function f(x) = $4x^2 + 4x-35$
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