Math Problem Statement

A graph of a the piecewise linear function 𝑓 (π‘₯) and table of the functions 𝑔(π‘₯) and 𝑔 β€² (π‘₯) are shown below. 1 (a) Given β„Ž(π‘₯) = 𝑓 (π‘₯) + 𝑔(π‘₯), find β„Ž β€² (1) (b) Given π‘˜(π‘₯) = 𝑓 (π‘₯)𝑔(π‘₯), find π‘˜ β€² (1). (c) Given 𝑙(π‘₯) = 𝑓 (π‘₯) 𝑔(π‘₯) , find 𝑙 β€² (3). (d) Given π‘š(π‘₯) = 𝑔(π‘₯) √ π‘₯ , find π‘šβ€² (4)

Solution

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Calculus
Derivatives
Sum Rule
Product Rule
Quotient Rule
Chain Rule

Formulas

Sum Rule: h'(x) = f'(x) + g'(x)
Product Rule: k'(x) = f'(x)g(x) + f(x)g'(x)
Quotient Rule: l'(x) = (f'(x)g(x) - f(x)g'(x)) / (g(x))^2
Chain Rule: Derivative of sqrt(x) = 1 / (2√x)

Theorems

Sum Rule
Product Rule
Quotient Rule
Chain Rule

Suitable Grade Level

Grades 11-12 (Advanced Calculus)