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Class 12 Mathematics Chapter 6 Applications Of Derivatives Quiz 2 (25 MCQs)

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1. Suppose that for a twice differentiable function f (x), f '(x) > 0 and f ''(x) > 0 on the interval (1, 3). If we use a linear approximation at x = 2 to estimate f (1.9), will that estimate be an underestimate or overestimate, and why?
2. The function $f\left(x\right)=e^x$ $f" \left(x\right)>0$
3. Refer to # 19.Determine the Displacement when the acceleration is 16 m/s$^{2}$
4. F(t) =2t$^{2}$-t+1 is the equation of Velocity. Determine the Acceleration Equation
5. Find the differential for the function y = cos(x)
6. A manager notices marginal cost rising sharply while marginal revenue is flat. Best short-run action?
7. Given revenue R(x)=100x-2x$^{2}$. The marginal revenue MR(x) is:
8. If f '(3) = 0 and f"(3) < 0, then which of the following must be true?
9. Marginal revenue (MR) is the derivative of total revenue with respect to quantity.
10. If f'(a) = 0 and f" (a) < 0, then x = a is the location of a relative
11. A car is moving away from a point at a rate of 60 km/h. If the car is 100 m away from the point, how fast is the distance from the car to a point 200 m away changing?
12. Apply optimization techniques to find the maximum area of a rectangle with a perimeter of 20.
13. What is the highest point on a function called?
14. The function h(x) is differentiable and decreasing for all real numbers. On what intervals is the function $y=h\left(x^3-4x^2\right)$
15. How many relative extrema does f have if $f'\left(x\right)=(x-2)^2(x+5)$
16. Find y' if y = cos$^{5}$(4x$^{3}$)
17. $\frac{\text{d}}{\text{d}x}\left[x^3\right]$
18. What is the decimal approximation of $\sqrt{52}$ $dy=f'(x)dx$
19. What is the "bottom of a valley" on a function (even if it is a cusp) called?
20. Given $g\left(x\right)=\frac{3}{x^2}-\frac{5}{x^4}+\frac{2}{x}$ $g^{" '}\left(x\right)$
21. Let f be a continuous function for which f(-2)=1 and f(5)=-3. The Intermediate Value Theorem guarantees that
22. Which statement is true about the slope of the tangent to a revenue curve at a point?
23. For a function f(x), f ' (-3) = 5 indicates f(x) is ..... at x=-3.
24. Discuss the concavity and the point(s) of inflection (if any) of the function:$f\left(x\right)=x^3-3x^2+10$
25. A particle moves along the x axis with its acceleration given by a(t) = t$^{2}$-2t for 0 < t < 6. At time t = 0, the velocity is 10. What is the maximum velocity of this particle on the specified interval?
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