University:
Missouri State University
Course:
MTH 136 | Precalculus 1
Academic year:

2021
Views:

205

Pages:

4
Author:

Cali Bowman

Calculus I UNIT 3: Derivative – QUIZ #2 REVIEW Name: _________________________ Date: _________________________ DERIVATIVE SHORTCUTS REVIEW Directions: Apply the appropriate algebraic derivatives rule(s) (Power/Product/Quotient/Chain Rule) to find 𝑓 ′ (𝑥) for each function. 1 1.) 𝑓(𝑥) = 2𝑥 3 − 8𝑥 2.) 𝑓(𝑥) = 3𝑥2 3.) 𝑓(𝑥) = (2𝑥 + 3)(6 − 𝑥 3 ) 4.) 𝑓(𝑥) = √𝑥 5 7𝑥+6 5.) 𝑓(𝑥) = 2𝑥4 −5𝑥 1 7.) 𝑓(𝑥) = (4𝑥+3)3 3 6.) 𝑓(𝑥) = 3 8.) 𝑓(𝑥) = 2 √𝑥 2 √𝑥 2 +3 3 3 9.) 𝑓(𝑥) = √(5𝑥 + 8)4 10.) 𝑓(𝑥) = (6𝑥2 −9)3 4𝑥 2 11.) 𝑓(𝑥) = (2𝑥−3)5 2 12.) 𝑓(𝑥) = (7𝑥+4) Directions: Find the slope of the tangent line for the following functions at the indicated 𝑥-value. 13.) 𝑓(𝑥) = 3𝑥 2 − 7 at 𝑥 = 2 14.) 𝑔(𝑥) = (8𝑥 2 + 7𝑥 + 1)5 at 𝑥 = −1 Directions: Find the point(s) on the graph of the function where the slope of the tangent line is indicated. 15.) Where does 𝑓(𝑥) = 𝑥3 3 − 4𝑥 have 𝑚 = 0? 16.) Where does 𝑔(𝑥) = −2 𝑥2 1 have 𝑚 = 2 Directions: Find the derivative of the following function, then calculate the slope of the tangent at the given 𝑥 value. 5 −7 3 17.) 𝑓(𝑥) = 𝑥 4 + 𝑥 3 − 𝑥 2 𝑥 = −1 18.) 𝑓(𝑥) = 2𝑥−4 𝑥−2 𝑥=4 Directions: Find the derivative of the following function, then find the point(s) where the slope of the tangent line is 16. 3 19.) 𝑔(𝑥) = 24√𝑥 2 Directions: Find the derivative of the following function. 3 20.) ℎ(𝑥) = 4𝑥 2 −7𝑥 22.) 𝑘(𝑥) = 2 5√𝑥 5 5 21.) 𝑗(𝑥) = (𝑥 2 +8)4 23.) 𝑦 = (3𝑥 2 + 2𝑥)(𝑥 4 − 3𝑥 + 1) Directions: Find the derivative of the following function using two different methods. 24.) 𝑦 = (𝑥 3 + 4)(2𝑥 2 − 𝑥) Directions: Find the derivative of 𝑔(𝑥). Then find the values of 𝑥 where the slope of the tangent line is 12. 25.) 𝑔(𝑥) = (4𝑥 + 2)3 Directions: Find the derivative of the following function. 2𝑥 26.) 𝑓(𝑥) = (6𝑥−1)4 SOLUTIONS 1.) 𝑓 ′ (𝑥) = 6𝑥 2 − 8 2.) 𝑓 ′ (𝑥) = −2 3𝑥 3 3.) 𝑓 ′ (𝑥) = −8𝑥 3 − 9𝑥 2 + 12 4.) 𝑓 ′ (𝑥) = 5 √𝑥 2 3 5.) 𝑓 ′ (𝑥) = −42𝑥 4 −48𝑥 3 +30 (2𝑥 4 −5𝑥)2 6.) 𝑓 ′ (𝑥) = 12 7.) 𝑓 ′ (𝑥) = − (4𝑥+3)4 8.) 𝑓 ′ (𝑥) = 3 3 −1 3√𝑥 3 −2𝑥 √(𝑥 2 +3)3 9.) 𝑓 ′ (𝑥) = 20 √5𝑥+8 3 10.) 𝑓 ′ (𝑥) = − (6𝑥2 108𝑥 −9)4 11.) 𝑓 ′ (𝑥) = 4(−8𝑥−3) (2𝑥−3)6 12.) 𝑓 ′ (𝑥) = − (7𝑥+4)3 56 13.) 𝑚 = 12 15.) (2, − 14.) 𝑚 = −720 16 16 ) & (−2, 3 ) 3 17.) 𝑓 ′ (𝑥) = − 19.) 𝑔′ (𝑥) = 20 𝑥5 + 1 16.) (2, − 2) 21 6 + 3 𝑥4 𝑥 18.) 𝑓 ′ (𝑥) = 0 𝑚 = 0 16 −24𝑥+21 20.) ℎ′ (𝑥) = (4𝑥2 −7𝑥)2 3 √𝑥 40𝑥 1 21.) 𝑗 ′ (𝑥) = − (𝑥 2 +8)5 22.) 𝑘 ′ (𝑥) = − 23.) 𝑦 ′ = 18𝑥 5 + 10𝑥 4 − 27𝑥 2 − 6𝑥 + 2 24.) 𝑦 ′ = 10𝑥 4 − 4𝑥 3 + 16𝑥 − 4 25.) 𝑔′ (𝑥) = 12(4𝑥 + 2)2 1 3 𝑥 = −4,−4 √𝑥 7 −36𝑥−2 26.) 𝑓 ′ (𝑥) = (6𝑥−1)5