Calculus I – Practice Quiz
1. The slope of the tangent line to the curve at a point is given by which derivative?
Answer: First derivative f′(x)f'(x)f′(x)
2. A function is concave upward on an interval if which condition holds?
Answer: f′′(x)>0f''(x) > 0f′′(x)>0
3. If limx→a−f(x)≠limx→a+f(x)\lim_{x \to a^-} f(x) \neq \lim_{x \to a^+}
f(x)limx→a− f(x) =limx→a+ f(x), what type of discontinuity occurs?
Answer: Jump discontinuity
4. The derivative of ekxe^{kx}ekx is?
Answer: kekxk e^{kx}kekx
5. What theorem guarantees that a continuous function on a closed interval attains
both a maximum and a minimum?
Answer: Extreme Value Theorem
6. If f′(c)=0f'(c) = 0f′(c)=0 and f′′(c)<0f''(c) < 0f′′(c)<0, what does f(c)f(c)f(c)
represent?
Answer: Local maximum
7. What is the derivative of ln(x)\ln(x)ln(x)?
Answer: 1x\frac{1}{x}x1
8. The limit of sinxx\frac{\sin x}{x}xsinx as x→0x \to 0x→0 equals?
Answer: 1
9. If a rational function has a degree in numerator greater than denominator, what
happens to horizontal asymptote?
Answer: No horizontal asymptote
10. The chain rule states: If y=f(u)y = f(u)y=f(u) and u=g(x)u = g(x)u=g(x), then
dydx=?\frac{dy}{dx} = ?dxdy =?
Answer: f′(u)⋅g′(x)f'(u) \cdot g'(x)f′(u)⋅g′(x)
1. The slope of the tangent line to the curve at a point is given by which derivative?
Answer: First derivative f′(x)f'(x)f′(x)
2. A function is concave upward on an interval if which condition holds?
Answer: f′′(x)>0f''(x) > 0f′′(x)>0
3. If limx→a−f(x)≠limx→a+f(x)\lim_{x \to a^-} f(x) \neq \lim_{x \to a^+}
f(x)limx→a− f(x) =limx→a+ f(x), what type of discontinuity occurs?
Answer: Jump discontinuity
4. The derivative of ekxe^{kx}ekx is?
Answer: kekxk e^{kx}kekx
5. What theorem guarantees that a continuous function on a closed interval attains
both a maximum and a minimum?
Answer: Extreme Value Theorem
6. If f′(c)=0f'(c) = 0f′(c)=0 and f′′(c)<0f''(c) < 0f′′(c)<0, what does f(c)f(c)f(c)
represent?
Answer: Local maximum
7. What is the derivative of ln(x)\ln(x)ln(x)?
Answer: 1x\frac{1}{x}x1
8. The limit of sinxx\frac{\sin x}{x}xsinx as x→0x \to 0x→0 equals?
Answer: 1
9. If a rational function has a degree in numerator greater than denominator, what
happens to horizontal asymptote?
Answer: No horizontal asymptote
10. The chain rule states: If y=f(u)y = f(u)y=f(u) and u=g(x)u = g(x)u=g(x), then
dydx=?\frac{dy}{dx} = ?dxdy =?
Answer: f′(u)⋅g′(x)f'(u) \cdot g'(x)f′(u)⋅g′(x)
