front 1 ![]() Consider the two functions shown below. Assume the blue line represents a(x) and the pink line represents b(x). Which statement is true about these functions at x=3? | back 1 ![]() |
front 2 Find the derivative of U(x) with respect to x for U(x)=4x2-3x+2. | back 2 ![]() dU/dx=8x-3 |
front 3 ![]() On the plot shown, assume the horizontal axis represents x and the vertical axis represents y. At what value of x does the function y(x) have a value of zero and a positive derivative? | back 3 The function y(x) is zero at x = 2 and at x = 6 But at x = 2, the function is decresing with negative slope===> negative derivative while at x = 6, the function is incresing with positive slope===> positive derivative |
front 4 ![]() We know that the velocity (v(t)) is the derivative of position (x(t)) with respect to time, meaning v(t) = dx/dt. Given that, what do we get if we integrate the velocity of an object from t=1 to t=4, meaning integral t=4 t=1 v(t)dt? | back 4 The change in the object’s position between t=1 and t=4 |
front 5 What is the derivative of B(t) with respect to t for B(t) = Asin(kx-omegat)? | back 5 ![]() dB/dt=-omegaAcos(kx-omegat) |
front 6 Find the derivative of y(x) with respect to x for y(x)=4+3x. | back 6 ![]() dy/dx=3 |
front 7 The potential energy of a particle experiencing a certain kind of force is given by U(x)=2x+(8/x) measured in joules (J), for positive values of x. What is the minimum potential energy this particle can have? | back 7 8 J |
front 8 What is the derivative of U(x) with respect to x for U(x)=10e5x? | back 8 ![]() dU/dx=50e5x |
front 9 What is the correct mathematical translation of the following sentence: “P is the derivative of W with respect to time (t).”? | back 9 P=dW/dt |
front 10 What is the rate of change of cos(x) with respect to x? | back 10 − |
front 11 ![]() On the plot shown, assume the horizontal axis represents x and the vertical axis represents y. What is true about the derivative of the function y(x) at x = 5? | back 11 The derivative of y(x) at x=5 is positive. |
front 12 The rate of change of quantity Z is also called its ______. | back 12 derivative Explanation: The rate of change of quantity Z with respect to time is also called its derivative. The integral of a quantity represents summing up the area under the function, not its rate of change. A cross product is a method of multiplying two vectors and is not a rate of change. A dot product is a method of multiplying two vectors and is not a rate of change. |
front 13 ![]() Which is the correct mathematical representation of the area indicated in the figure? | back 13 ![]() The area under a curve is the integral of the function over the indicated range. |
front 14 Find the derivative of f(t) with respect to t for f(t)=10t10. | back 14 Differentiate using the power rule, d/dx[xn]=nxn-1. df/dt=10 x 10 t (10-1) df/dt=100t9 |
front 15 What is d/dx sin(x)? | back 15 cos(x) |
front 16 The force exerted on a particle experiencing a certain kind of force is given by F(t)=-3t4+8t3+5, with F measured in newtons (N) and t measured in s. At what time is the most force exerted on the particle? | back 16 At about t=2 seconds |
front 17 ![]() Consider the two functions shown below. Assume the blue line represents a(x) and the pink line represents b(x). Which statement is true about these functions at x=4.5? | back 17 ![]() |
front 18 What is the derivative of E(x) with respect to x for E(x)=Acos(kx)? | back 18 dE/dx=-kAsin(kx) |
front 19 ![]() On the plot shown, assume the horizontal axis represents x and the vertical axis represents y. At what value of x does the function y(x) have a non-zero value and a zero derivative? | back 19 At x=4 |
front 20 Find the derivative of a(y) with respect to y for a(y)=2/y2 (1+(2y3/5)-(5/y4)). | back 20 ![]() da/dy=(-4/y3)+(4/5)+(60/y7) |
front 21 ![]() What is the correct mathematical translation of the following sentence: “W is the integral of F with respect to distance (x).”? | back 21 ![]() |
front 22 ![]() Consider the two functions shown below. Assume the blue line represents a(x) and the pink line represents b(x). How do the second derivatives of the two functions with respect to x compare? | back 22 ![]() |
front 23 At what value of t will the function v(t)=-3/t2 be parallel to the function omega(t)=(3t/4)-5? | back 23 t=2 |
front 24 Find the derivative of y(x) with respect to x for y(x)=4+3x. | back 24 ![]() dy/dx=3 |
front 25 What is the derivative of v(t) with respect to t for v(t)=3et. | back 25 ![]() dv/dt=v(t)=3et |
front 26 Find the derivative of B(t) with respect to t for | back 26 B(t) = 1/t3 - 1/t5 + 1/t dB/dt = = (-3/t4)+ (5/t6)-(1/t2) |