Definition of Derivative

Derivative means the same thing as

• slope of the tangent line
• slope of the normal line
• exponent
• potato

Tags

CCSS.HSS.ID.C.7

The derivative of a function is its

• Slope
• Maximum/Minimum
• Instantaneous rate of change
• Common Denominator

Given a function, f(x), if f'(x)>0 over a certain interval, then f(x) is __________ over that interval.

• increasing
• decreasing
• concave up
• concave down

• 15x²

• (5/4)x⁴

• indeterminate

• ∞

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.1

f'(x)=

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

• $\lim_{x\rightarrow c}\left(\frac{f\left(x\right)-f\left(c\right)}{x-c}\right)$

• $\frac{\text{d}y}{\text{d}x}$

• an equation for the slope of the tangent line

 $\lim_{h\rightarrow0}\left(\frac{5\left(x+h\right)^2-5x^2}{h}\right)$  

•  $5x^2$  

•  $10x$  

• 10

• DNE

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

 $\frac{\text{d}}{\text{d}x}\left[x^3\right]$  

•  $6x$  

• 3

•  $3x^2$  

• 6

 $\lim_{x\rightarrow2}\left(\frac{x^2-4}{x-2}\right)$  

• 2

• 4

• 6

• 8

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

 $\lim_{x\rightarrow\infty}x^2+3x-5$  

•  $-\infty$  

• 2

• 0

•  $\infty$  

 $\lim_{x\rightarrow\infty}\left(\frac{x^2+x-3}{x^4-x^3+1}\right)$  

•  $-\infty$  

• 0

• 1

•  $\infty$  

Tags

CCSS.HSA.APR.D.7