Calculus Quiz 1

Differentiate y= 12x^-2

• 24x^-1
• -24x^-3
• -24x^-1
• 6x^-3

Derivative of 1/x is....

• -1/x²

• 1/x²

• 1

• none of these

Derivative of √x is ....

• -1/(2√x)

• 1/(2√x)

• 2/(√x)

• -2/(√x)

What is the derivative of xⁿ?

• (n-1)xⁿ
• nxⁿ⁺¹
• (n+1)x^n-1
• nx^n-1

Which one is the correct formula for The First Principle of Differentiation ?

• $f'\left(x\right)=\lim_{h\rightarrow0}\frac{f\left(x+h\right)+f\left(x\right)}{h}$

• $f'\left(x\right)=\lim_{h\rightarrow0}\ \frac{f\left(x\right)+f\left(x+h\right)}{h}$

• $f'\left(x\right)=\lim_{h\rightarrow0}\ \frac{f\left(x+h\right)-f\left(x\right)}{h}$

• $f'\left(x\right)=\lim_{h\rightarrow0}\ \frac{f\left(x\right)-f\left(x+h\right)}{h}$

If log₃x=2, then

• 3^x=2
• 2^x=3
• 3²=x
• 3^x=9

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.

• increasing
• decreasing
• concave up
• concave down

If a function's FIRST derivative is negative at a certain point, what does that tell you?

• The function is increasing at that point
• The function is decreasing at that point
• The concavity of the function is up at that point
• The concavity of the function is down at that point

Tags

CCSS.HSF.IF.B.4

What is the maximum value of f(x) = x³ - 3x² - 1 on the interval [-3, 2]?

• 0
• -1
• 2
• 5

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7