Mini Quiz- Integration and Derivatives

Multiple Choice

Find the derivative
f(t) = (t² + 2t)⁵

• f'(t) = 5(2t+2)⁴

• f'(t) = 5(t² + 2t)⁴

•  f'(t) = 5(t² + 2t)⁴(2t)

• f'(t) = 5(t² + 2t)⁴(2t + 2)

Multiple Choice

Derivative means the same thing as

• slope of the tangent line

• slope of the normal line

• slope of the secant line

• the function’s value

Multiple Choice

What is the derivative of f(x)= cx?

• c

• x

• 1

• 0

Multiple Choice

Given f(x) = ax² + 2bx. What are a and b if f'(x) = 8x + 6?

• a = 2 and b = 3

• a = 3 and b = 2

• a = 3 and b = 4

• a = 4 and b = 3

Multiple Choice

What is the derivative?

• A

• B

• C

• D

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Find the derivative of $$f\left(x\right)=\frac{3x+5}{x^2+4}$$  

• $$f'\left(x\right)=\frac{3x^2-10x+12}{\left(x^2+4\right)^2}$$  

• $$f'\left(x\right)=\frac{-3x^2-10x+12}{\left(x^2+4\right)^2}$$  

• $$f'\left(x\right)=\frac{3x^2-10x+12}{\left(x^2+4\right)^{ }}$$  

• $$f'\left(x\right)=\frac{-3x^2-10x-12}{\left(x^2+4\right)^2}$$  

Multiple Choice

• A

• B

• C

• E

Multiple Choice

$$\int\left(6\sqrt{x}-1\right)dx$$  

• $$6x^{\frac{3}{2}}+x+C$$  

• $$4x^{\frac{3}{2}}-x+C$$  

• $$3x^{-\frac{1}{2}}-x+C$$  

• I didn't look at my notes to see how to do this one.

Multiple Choice

$$\int\left(\frac{1}{x^2}+\frac{6}{x^3}\right)dx$$  

• $$-x^{-1}-3x^{-2}+C$$  

• $$\frac{x^{-3}}{-3}+\frac{6x^{-4}}{-4}+C$$  

• $$-x^{-1}-3x^{-2}$$  

• $$-x-3x^2+C$$