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Class 12 Mathematics Chapter 6 Applications Of Derivatives Quiz 9 (10 MCQs)

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1. The line y = mx + 1 is a tangent to the curve y$^{2}$ = 4x, if the value of m is
2. Nature of the function f(x) = e$^{2x}$ is .....
3. $\lim_{x\rightarrow2}\left(\frac{x^2-4}{x-2}\right)$
4. Identify the critical points of the following function:$^{}$g(x)=2x$^{3}$-3x$^{2}$
5. In a cone, find the rate of change of the volume if dr/dt is 2 inches per minute and the height is 3r when the radius is 6.
6. TRUE OR FALSE? If f is continuous on [-1, 1], f(-1)=4 and f(1)=-2, then there is a zero between-1 and 1.
7. Which of the following theorems may be applied to the function $y=\left|x-3\right|+b, \\b>0, $
8. A rectangular solid that has a square base has a surface area of 150 square inches. Find the maximum volume of the solid. (use Calculus)
9. Given the function $u(x) = \ln(x)-x + 2$ $x = 1$
10. Rachel is standing atop a 13ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3ft/sec. How fast is the angle changing between the base of the ladder and the ground when the ladder is 5 ft high?
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