Mathematics

Problem

Consider a differentiable function

y=f(x)

whose derivative is given by

\dfrac{dy}{dx}=4x+1

. a. (i) Rewrite the derivative in Lagrange notation. b. (ii) Find the numerical value of the derivative at

x=2

using both notations. c. (iii) Describe, without calculation, the nature (increasing or decreasing) of the function for

x>-\dfrac{1}{4}

, justifying your answer through the signs of the two notations used.