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DERIVATIVE RULES
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TRUE or FALSE. The derivative of 5 𝑥^3 is 15 𝑥^2..
TRUE
What is the derivative of 𝑓 ( 𝑥 ) = 𝑥
1
What rule is applied to find the derivative of 𝑓 ( 𝑥 ) = 3 𝑥^ 2 − 5 𝑥 ? A. Chain Rule B. Product Rule C. Sum/Difference Rule D. Quotient Rule
C. Sum/Difference Rule
If 𝑓 ′ ( 𝑥 ) > 0 on an interval, the function is ______. a) Constant b) Increasing c) Decreasing d) Undefined
b) Increasing
If the derivative of a function is zero at a point, the tangent line is a) Vertical b) Slanted c) Horizontal d) Undefined
c) Horizontal
Differentiate f(x)=x^3 −7x.
3x^2−7
Find the derivative of f(x)=4x^3 −2x+1.
12x^2−2
If a function has a positive derivative, the function is ______. a) Constant b) Increasing c) Decreasing d) Undefined
b) Increasing
The derivative of a function at a point gives the ________ of the tangent line. a) Length b) Area c) Slope d) Intercept
c) Slope
Find the derivative of 𝑓 ( 𝑥 ) = 3 𝑥^2. a) 6x b) 3x c) 6 𝑥 ^2 d) 𝑥 ^2
a) 6x
Which rule is used to find the derivative of 𝑓 ( 𝑥 ) = 7 𝑥 ^4 ?
Power Rule
The derivative of a constant is always ________.
Zero
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