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Match each function (a, b, c, d) with its derivative and explain how you knew. Not all derivatives will be used. Functions: 8x² + 2x - a) x3 b) sin(x) c) log(x) d) 25x+3 - 5

Match each function (a, b, c, d) with its derivative and explain how you knew. Not all derivatives will be used. Functions: 8x² + 2x - a) x3 b) sin(x) c) log(x) d) 25x+3 - 5

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Match each function (a, b, c, d) with its derivative and explain how you knew. Not all derivatives will be used. Functions: - a) x³ b) sin(x) c) log(x) d) 25x+3 8x² + 2x - 5
Transcribed Image Text:Match each function (a, b, c, d) with its derivative and explain how you knew. Not all derivatives will be used. Functions: - a) x³ b) sin(x) c) log(x) d) 25x+3 8x² + 2x - 5
Derivatives: ii) i) Quadratic with minimum around x = 1 Increasing exponential with y-intercept 8 iv) Sine function vi) iii) Cosine function v) Cosine function, reflected over the x- axis vii) Increasing exponential with y-intercept around 30, point around 1, 900 Top right quadrant of a reciprocal function viii) Cubic with max around x = -1.5, min around x = 1.5
Transcribed Image Text:Derivatives: ii) i) Quadratic with minimum around x = 1 Increasing exponential with y-intercept 8 iv) Sine function vi) iii) Cosine function v) Cosine function, reflected over the x- axis vii) Increasing exponential with y-intercept around 30, point around 1, 900 Top right quadrant of a reciprocal function viii) Cubic with max around x = -1.5, min around x = 1.5
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Step 1: Question Description

Match each function (a, b, c, d) with its derivative and explain how we knew.

Not all derivatives will be used.

Functions:

a) x cubed minus 8 x squared plus 2 x minus 5

b) sin open parentheses x close parentheses

c) log open parentheses x close parentheses

d) 2 to the power of 5 x plus 3 end exponent


Derivatives:

i) Quadratic with minimum around x equals 1.

ii) Increasing exponential with y-intercept 8.

iii) Cosine function.

iv) Sine function.

v) Cosine function, reflected over the x-axis.

vi) Top right quadrant of a reciprocal function.

vii) Increasing exponential with y-intercept around 30, point around 1 comma space 900.

viii) Cubic with max around x equals negative 1.5, min around x equals 1.5

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