Definition of a 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

Tags

CCSS.HSF.IF.B.4

• 15x²

• (5/4)x⁴

• indeterminate

• ∞

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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

It's the average rate of change of y=3x^2+4x-2 on the interval [-2, 1].

• 0

• 1

• 2

• 3

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CCSS.HSF.IF.B.6

Use the definition of the derivative (aka the limit process) to find the derivative of y=x^2+9 (be ready to show work on the test).

• x^2

• 2x+9

• 2

• 2x

This is NOT a correct notation for a derivative

• y ' (say it as "y prime")

• f '(x) (say it as "f prime of x")

• dy/dx

• dx/dy

Use the definition of the derivative (aka the limit process) to find the derivative of y=x^2-2x+3 (be ready to show work on the test).

• y ' = 2x - 2

• y ' = 2x^2

• y ' = 2x

• y ' = x^2

Write the slope of the line tangent to the graph of y=x^2-2 at the point x = 8.

• 2

• -4

• -8

• -16