Class 11 Mathematics Chapter 13 Limits And Derivatives Quiz 4 (25 MCQs)

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1. FInd the derivative:$f\left(x\right)=-\frac{2}{3}x^3-\frac{1}{2}x^2+9x$
2. The position of an object in feet after t seconds is given by $s\left(t\right)=16t^2-\frac{1}{2}t^3$
3. If $f\left(x\right)=-3x^2+6x-4$ $f'\left(x\right).$
4. What is the equation of the tangent to the curve f(x)= 4x$^{2}$+2x-1 at the point x=0?
5. Find the derivative of the given equation $f\left(x\right)=4x$
6. Find f'(x) for the function, then find f'(x) for the given x.-f(x) = 5x + 9, f'(2)
7. Find the antiderivative of f(x) = x$^{3}$-2x$^{2}$ + 4x-5.
8. If a function has a derivative that is negative, what does that tell you?
9. $\lim_{x\rightarrow\infty}\\frac{1-2x+2x^3}{x^3+x+1}=\ ..... $
10. Find dy/dx by Implicit Differentiation x$^{3}$ +y$^{3}$$^{ }$ = 36
11. Which of the following statements is true about the limit $\lim_{x \to a} f(x)$
12. If the graph of a function has a sharp corner at $x = 2$ $x = 2$
13. 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?
14. $Evaluate\\lim_{x\rightarrow3}\left[\frac{x^2-9}{x-3}\right]$
15. What is the derivative of sec(x)?
16. $\lim_{x\rightarrow2}=\frac{x^4-16}{x-2}$
17. What is the derivative of cot(x)?
18. $Evaluate\\lim_{x\rightarrow1}\\frac{x^2+1}{x+100}$
19. $A'=\frac{-2\left(x-12\right)\left(x+12\right)}{x^2}$
20. If y=2x-8, what is the minimum value of the product xy?
21. Use the derivative rules to find the derivative of the function f(x) = (3x-4)$^{2}$
22. Find the derivative $x^2\left(-3x^2-2\right)$
23. Find the derivative of the given equationf(x) = 1/x$^{2}$
24. Evaluate $\lim_{x\rightarrow1}\left(x^2-2x+1\right)$
25. $\lim_{x\rightarrow3}=\frac{\sqrt[]{x+6}-x}{x-3}$